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Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-03-04 Sunghan Kim, Kaj Nyström
We prove new optimal regularity results for obstacle problems involving evolutionary -Laplace type operators in the degenerate regime . Our main results include the optimal regularity improvement at free boundary points in intrinsic backward -paraboloids, up to the critical exponent, , and the optimal regularity across the free boundaries in the full cylinders up to a universal threshold. Moreover
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The existence of a weak solution for a compressible multicomponent fluid structure interaction problem J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-03-04 Martin Kalousek, Sourav Mitra, Šárka Nečasová
We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modeled by a system resembling compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. The shell possesses a non-linear
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On nonlinear instability of Prandtl's boundary layers: The case of Rayleigh's stable shear flows J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-03-02 Emmanuel Grenier, Toan T. Nguyen
In 1904, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of Navier Stokes equations near a boundary as the viscosity goes to 0. His Ansatz has later been justified for analytic data by R.E. Caflisch and M. Sammartino. In this paper, we prove that his expansion is false, up to order terms in norm, in the case of solutions with Sobolev regularity, even in cases
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Fast fusion in a two-dimensional coagulation model J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-03-01 Iulia Cristian, Juan J.L. Velázquez
In this work, we study a particular system of coagulation equations characterized by two values, namely volume and surface area . Compared to the standard one-dimensional models, this model incorporates additional information about the geometry of the particles. We describe the coagulation process as a combination between collision and fusion of particles. We prove that we are able to recover the standard
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A geometrisation of [formula omitted]-manifolds J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-03-01 M. Heuer, M. Jotz
This paper proposes a of -manifolds of degree as -fold vector bundles equipped with a (signed) -symmetry. More precisely, it proves an equivalence between the categories of -manifolds and the category of (signed) symmetric -fold vector bundles, by finding that symmetric -fold vector bundle cocycles and -manifold cocycles are identical.
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Minimal solutions of master equations for extended mean field games J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-03-01 Chenchen Mou, Jianfeng Zhang
In an extended mean field game the vector field governing the flow of the population can be different from that of the individual player at some mean field equilibrium. This new class strictly includes the standard mean field games. It is well known that, without any monotonicity conditions, mean field games typically contain multiple mean field equilibria and the wellposedness of their corresponding
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Migrating elastic flows J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-03-01 Tomoya Kemmochi, Tatsuya Miura
Huisken's problem asks whether there is an elastic flow of closed planar curves that is initially contained in the upper half-plane but ‘migrates’ to the lower half-plane at a positive time. Here we consider variants of Huisken's problem for open curves under the natural boundary condition, and construct various migrating elastic flows both analytically and numerically.
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Borel (α,β)-multitransforms and Quantum Leray–Hirsch: integral representations of solutions of quantum differential equations for P1-bundles J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-01-30 Giordano Cotti
In this paper, we address the integration problem of the isomonodromic system of quantum differential equations (qDEs) associated with the quantum cohomology of P1-bundles on Fano varieties. It is shown that bases of solutions of the qDE associated with the total space of the P1-bundle can be reconstructed from the datum of bases of solutions of the qDE associated with the base space. This represents
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Nonlocal critical growth elliptic problems with jumping nonlinearities J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-01-30 Giovanni Molica Bisci, Kanishka Perera, Raffaella Servadei, Caterina Sportelli
In this paper we study a nonlocal critical growth elliptic problem driven by the fractional Laplacian in the presence of a jumping nonlinearity. By using variational and topological methods and applying some new linking theorems recently proved by Perera and Sportelli in [19], we prove the existence of a nontrivial solution for the problem under consideration. The results we obtain here are the nonlocal
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On the Almgren minimality of the product of a paired calibrated set with a calibrated set of codimension 1 with singularities, and new Almgren minimal cones J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-02-02 Xiangyu Liang
In this paper, we prove that the product of a paired calibrated set and a set of codimension 1 calibrated by a coflat calibration with small singularity set is Almgren minimal. This is motivated by the attempt to classify all possible singularities for Almgren minimal sets–Plateau's problem in the setting of sets. In particular, a direct application of the above result leads to various types of new
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The primitive equations with stochastic wind driven boundary conditions J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-02-01 Tim Binz, Matthias Hieber, Amru Hussein, Martin Saal
The primitive equations for geophysical flows are studied under the influence of modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary value problems to define a notion of solutions. Then a rigorous treatment of these stochastic boundary conditions, which combines stochastic and deterministic methods, yields that these equations admit a unique
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A global branch approach to normalized solutions for the Schrödinger equation J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-02-01 Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schrödinger equation of the form Our approach permits to handle in a unified way nonlinearities which are either mass subcritical, mass critical or mass supercritical. Among its main ingredients is the study of the asymptotic behaviors of the positive solutions as or and the existence of an unbounded continuum
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Stability of the separable solutions for a nonlinear boundary diffusion problem J. Math. Pures Appl. (IF 2.3) Pub Date : 2024-02-01 Tianling Jin, Jingang Xiong, Xuzhou Yang
In this paper, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the asymptotic behavior of its solutions, and prove the stability of its separable solutions.
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C1,α-regularity for solutions of degenerate/singular fully nonlinear parabolic equations J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-06 Ki-Ahm Lee, Se-Chan Lee, Hyungsung Yun
We establish the interior C1,α-estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equationsut=|Du|γF(D2u)+fin Q1, where γ>−1 and f∈C(Q1)∩L∞(Q1). For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem{ut=(1+|Du|2)γ/2F(D2u)in Q1u=φon ∂pQ1, where γ>−2. Our approach utilizes the Bernstein method with approximations in view of the difference
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On the weak solutions for the MHD systems with controllable total energy and cross helicity J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-06 Changxing Miao, Weikui Ye
In this paper, we prove the non-uniqueness of three-dimensional magneto-hydrodynamic (MHD) system in C([0,T];L2(T3)) for any initial data in Hβ¯(T3) (β¯>0), by exhibiting that the total energy and the cross helicity can be controlled in a given positive time interval. Our results extend the non-uniqueness results of the ideal MHD system to the viscous and resistive MHD system. Different from the ideal
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Far field broadband approximate cloaking for the Helmholtz equation with a Drude-Lorentz refractive index J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-06 Fioralba Cakoni, Narek Hovsepyan, Michael S. Vogelius
This paper concerns the analysis of a passive, broadband approximate cloaking scheme for the Helmholtz equation in Rd for d=2 or d=3. Using ideas from transformation optics, we construct an approximate cloak by “blowing up” a small ball of radius ϵ>0 to one of radius 1. In the anisotropic cloaking layer resulting from the “blow-up” change of variables, we incorporate a Drude-Lorentz-type model for
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Asymptotic behavior of a plate with a non-planar top surface J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-06 G. Griso
In this paper, we study the asymptotic behaviors of a plate with non-planar top surface in the framework of linear elasticity. For this plate, we give a decomposition of the displacements. We show that every displacement of the plate is the sum of a Kirchhoff-Love displacement and a residual displacement that takes into account the deformations of the fibers of the plate and shear. We also prove Korn's
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High-order estimates for fully nonlinear equations under weak concavity assumptions J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-06 Alessandro Goffi
This paper studies a priori and regularity estimates of Evans-Krylov type in Hölder spaces for fully nonlinear uniformly elliptic and parabolic equations of second order when the operator fails to be concave or convex in the space of symmetric matrices. In particular, it is assumed that either the level sets are convex or the operator is concave, convex or close to a linear function near infinity.
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Khovanskii bases for semimixed systems of polynomial equations – Approximating stationary nonlinear Newtonian dynamics J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-06 Viktoriia Borovik, Paul Breiding, Javier del Pino, Mateusz Michałek, Oded Zilberberg
We provide an approach to counting roots of polynomial systems, where each polynomial is a general linear combination of prescribed, fixed polynomials. Our tools rely on the theory of Khovanskii bases, combined with toric geometry, the Bernstein–Khovanskii–Kushnirenko (BKK) Theorem, and fiber products. As a direct application of this theory, we solve the problem of counting the number of approximate
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Local well-posedness of the free-boundary incompressible magnetohydrodynamics with surface tension J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-05 Xumin Gu, Chenyun Luo, Junyan Zhang
We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the ideas developed in the remarkable paper [11] by Coutand and Shkoller to generate an approximate problem with artificial viscosity indexed by κ>0 whose solution converges
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Caffarelli-Kohn-Nirenberg identities, inequalities and their stabilities J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-05 Cristian Cazacu, Joshua Flynn, Nguyen Lam, Guozhen Lu
We set up a one-parameter family of inequalities that contains both the Hardy inequalities (when the parameter is 1) and the Caffarelli-Kohn-Nirenberg inequalities (when the parameter is optimal). Moreover, we study these results with the exact remainders to provide direct understandings to the sharp constants, as well as the existence and non-existence of the optimizers of the Hardy inequalities and
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Regularity theory for parabolic systems with Uhlenbeck structure J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-05 Jihoon Ok, Giovanni Scilla, Bianca Stroffolini
We establish local regularity theory for parabolic systems of Uhlenbeck type with φ-growth. In particular, we prove local boundedness of weak solutions and their gradient, and then local Hölder continuity of the gradients, providing suitable assumptions on the growth function φ. Our approach, being independent of the degeneracy of the system, allows for a unified treatment of both the degenerate and
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Nonautonomous (p,q)-equations with unbalanced growth and competing nonlinearities J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-12-05 Zhenhai Liu, Nikolaos S. Papageorgiou
We consider a parametric nonlinear Dirichlet problem driven by the double phase differential operator and a reaction that has the competing effects of parametric “concave” term and of a “convex” perturbation (concave-convex problem). Using variational tools together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at
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Homogenization of Schrödinger equations. Extended effective mass theorems for non-crystalline matter J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 Vernny Ccajma, Wladimir Neves, Jean Silva
This paper concerns the homogenization of Schrödinger equations for non-crystalline matter, that is to say the coefficients are given by the composition of stationary functions with stochastic deformations. Two rigorous results of so-called effective mass theorems in solid state physics are obtained: a general abstract result (beyond the classical stationary ergodic setting), and one for quasi-perfect
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Overdetermined elliptic problems in nontrivial contractible domains of the sphere J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 David Ruiz, Pieralberto Sicbaldi, Jing Wu
In this paper, we prove the existence of nontrivial contractible domains Ω⊂Sd, d≥2, such that the overdetermined elliptic problem{−εΔgu+u−up=0in Ω, u>0in Ω, u=0on ∂Ω, ∂νu=constanton ∂Ω, admits a positive solution. Here Δg is the Laplace-Beltrami operator in the unit sphere Sd with respect to the canonical round metric g, ε>0 is a small real parameter and 11 if d=2). These domains are perturbations
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Generic uniqueness for the Plateau problem J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 Gianmarco Caldini, Andrea Marchese, Andrea Merlo, Simone Steinbrüchel
Given a complete Riemannian manifold M⊂Rd which is a Lipschitz neighborhood retract of dimension m+n, of class Ch,β and an oriented, closed submanifold Γ⊂M of dimension m−1, which is a boundary in integral homology, we construct a complete metric space B of Ch,α-perturbations of Γ inside M, with α<β, enjoying the following property. For the typical element b∈B, in the sense of Baire categories, there
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Stability of the scattering transform for deformations with minimal regularity J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 Fabio Nicola, S. Ivan Trapasso
The wavelet scattering transform introduced by Stéphane Mallat is a unique example of how the ideas of harmonic and multiscale analysis can be ingeniously exploited to build a signal representation with provable geometric stability properties, such as the Lipschitz continuity to the action of small C2 diffeomorphisms – a remarkable result for both theoretical and practical purposes, inherently depending
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Weyl's law for singular Riemannian manifolds J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 Y. Chitour, D. Prandi, L. Rizzi
We study the asymptotic growth of the eigenvalues of the Laplace-Beltrami operator on singular Riemannian manifolds, where all geometrical invariants appearing in classical spectral asymptotics are unbounded, and the total volume can be infinite. Under suitable assumptions on the curvature blow-up, we show how the singularity influences the Weyl's asymptotics. Our main motivation comes from the construction
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Convergence of the solutions of the nonlinear discounted Hamilton–Jacobi equation: The central role of Mather measures J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 Qinbo Chen, Albert Fathi, Maxime Zavidovique, Jianlu Zhang
Given a continuous Hamiltonian H:(x,p,u)↦H(x,p,u) defined on T⁎M×R, where M is a closed connected manifold, we study viscosity solutions, uλ:M→R, of discounted equations:H(x,dxuλ,λuλ(x))=cin M where λ>0 is called a discount factor and c is the critical value of H(⋅,⋅,0). When the Hamiltonian H is convex and superlinear in p and non–decreasing in u, under an additional non–degeneracy condition, we obtain
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Control of neural transport for normalising flows J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 Domènec Ruiz-Balet, Enrique Zuazua
Inspired by normalising flows, we analyse the bilinear control of neural transport equations by means of time-dependent velocity fields restricted to fulfil, at any time instance, a simple neural network ansatz. The L1 approximate controllability property is proved, showing that any probability density can be driven arbitrarily close to any other one in any time horizon. The control vector fields are
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The locally homeomorphic property of McKean-Vlasov SDEs under the global Lipschitz condition J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 Xianjin Cheng, Zhenxin Liu
In this paper, we establish the locally diffeomorphic property of the solution to McKean-Vlasov stochastic differential equations defined in the Euclidean space. Our approach is built upon the insightful ideas put forth by Kunita. We observe that although the coefficients satisfy the global Lipschitz condition and some suitable regularity condition, the solution in general does not satisfy the globally
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Rigidity of weighted Einstein smooth metric measure spaces J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-11-07 Miguel Brozos-Vázquez, Diego Mojón-Álvarez
We study the geometric structure of weighted Einstein smooth metric measure spaces with weighted harmonic Weyl tensor. A complete local classification is provided, showing that either the underlying manifold is Einstein, or decomposes as a warped product in a specific way. Moreover, if the manifold is complete, then it either is a weighted analogue of a space form, or it belongs to a particular family
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Products and commutators of martingales in H1 and BMO J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-10-31 Aline Bonami, Yong Jiao, Guangheng Xie, Dachun Yang, Dejian Zhou
Let f:=(fn)n∈Z+ and g:=(gn)n∈Z+ be two martingales related to the probability space (Ω,F,P) equipped with the filtration (Fn)n∈Z+. Assume that f is in the martingale Hardy space H1 and g is in its dual space, namely the martingale BMO. Then the semi-martingale f⋅g:=(fngn)n∈Z+ may be written as the sumf⋅g=G(f,g)+L(f,g). Here L(f,g):=(L(f,g)n)n∈Z+ with L(f,g)n:=∑k=0n(fk−fk−1)(gk−gk−1)) for any n∈Z+,
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Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-25 Théophile Chaumont-Frelet, Andrea Moiola, Euan A. Spence
We consider the time-harmonic Maxwell equations posed in R3. We prove a priori bounds on the solution for L∞ coefficients ϵ and μ satisfying certain monotonicity properties, with these bounds valid for arbitrarily-large frequency, and explicit in the frequency and properties of ϵ and μ. The class of coefficients covered includes (i) certain ϵ and μ for which well-posedness of the time-harmonic Maxwell
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Equilibrium in two-player stochastic games with shift-invariant payoffs J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-25 János Flesch, Eilon Solan
We show that every two-player stochastic game with finite state and action sets, and bounded, Borel-measurable, and shift-invariant payoffs, admits an ε-equilibrium for all ε>0.
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Geometric bounds for the magnetic Neumann eigenvalues in the plane J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-21 Bruno Colbois, Corentin Léna, Luigi Provenzano, Alessandro Savo
We consider the eigenvalues of the magnetic Laplacian on a bounded domain Ω of R2 with uniform magnetic field β>0 and magnetic Neumann boundary conditions. We find upper and lower bounds for the ground state energy λ1 and we provide semiclassical estimates in the spirit of Kröger for the first Riesz mean of the eigenvalues. We also discuss upper bounds for the first eigenvalue for non-constant magnetic
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Global well-posedness of the 1d compressible Navier–Stokes system with rough data J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-21 Ke Chen, Ly Kim Ha, Ruilin Hu, Quoc-Hung Nguyen
In this paper, we study the global well-posedness problem for the 1d compressible Navier–Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (2022) [30] established the global well-posedness theory for the 1d isentropic cNSE with initial velocity data in BV space. Then, it was extended to the 1d full cNSE with initial velocity and temperature data in BV space by Wang et
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Bounded Poincaré operators for twisted and BGG complexes J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Andreas Čap, Kaibo Hu
We construct bounded Poincaré operators for twisted complexes and BGG complexes with a wide class of function classes (e.g., Sobolev spaces) on bounded Lipschitz domains. These operators are derived from the de Rham versions using BGG diagrams and, for vanishing cohomology, satisfy the homotopy identity dP+Pd=I in degrees >0. The operators preserve polynomial classes if the de Rham versions do so.
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Stability threshold of Couette flow for 2D Boussinesq equations in Sobolev spaces J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Zhifei Zhang, Ruizhao Zi
Consider the nonlinear stability of the Couette flow in the Boussinesq equations with vertical dissipation on T×R. We prove that if the initial perturbations uin and θin to the Couette flow vs=(y,0)⊤ and θs=1, respectively, satisfy ‖uin‖HN+1+ν−12‖θin‖HN+ν−13‖|∂x|13θ‖HN≪ν13, N>7, then the resulting solution remains close to the Couette flow in L2 at the same order for all time.
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Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Jørgen Endal, Liviu I. Ignat, Fernando Quirós
We study the large-time behaviour of nonnegative solutions to the Cauchy problem for a nonlocal heat equation with a nonlinear convection term. The diffusion operator is the infinitesimal generator of a stable Lévy process, which may be highly anisotropic. The initial data are assumed to be bounded and integrable. The mass of the solution is conserved along the evolution, and the large-time behaviour
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Local orthogonal maps and rigidity of holomorphic mappings between real hyperquadrics J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Yun Gao, Sui-Chung Ng
We propose a coordinate-free approach to study the holomorphic maps between the real hyperquadrics in complex projective spaces. It is based on a notion of orthogonality on the projective spaces induced by the Hermitian structures that define the hyperquadrics. There are various kinds of special linear subspaces associated to this orthogonality which are well respected by the relevant holomorphic maps
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On the global-in-time inviscid limit of the 3D degenerate compressible Navier-Stokes equations J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Yongcai Geng, Yachun Li, Shengguo Zhu
In this paper, the global-in-time inviscid limit of the three-dimensional (3D) isentropic compressible Navier-Stokes equations is considered. First, when viscosity coefficients are given as a constant multiple of density's power ((ρϵ)δ with δ>1), for regular solutions to the corresponding Cauchy problem, via introducing one “quasi-symmetric hyperbolic”–“degenerate elliptic” coupled structure to control
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On the derived category of the Cayley Grassmannian J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Lyalya Guseva
We construct a full exceptional collection consisting of vector bundles in the derived category of coherent sheaves on the so-called Cayley Grassmannian, the subvariety of the Grassmannian Gr(3,7) parameterizing 3-subspaces that are annihilated by a general 4-form. The main step in the proof of fullness is a construction of two self-dual vector bundles which is obtained from two operations with quadric
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Existence and non-existence of minimal graphs J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Qi Ding, J. Jost, Y.L. Xin
We study the Dirichlet problem for minimal surface systems in arbitrary dimension and codimension via mean curvature flow, and obtain the existence of minimal graphs over arbitrary mean convex bounded C2 domains for a large class of prescribed boundary data. This result can be seen as a natural generalization of the classical sharp criterion for solvability of the minimal surface equation by Jenkins-Serrin
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Uniqueness, multiplicity and nondegeneracy of positive solutions to the Lane-Emden problem J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Houwang Li, Juncheng Wei, Wenming Zou
In this paper, we study the nearly critical Lane-Emden equations(⁎){−Δu=up−εinΩ,u>0inΩ,u=0on∂Ω, where Ω⊂RN with N≥3, p=N+2N−2 and ε>0 is small. Our main result is that when Ω is a smooth bounded convex domain and the Robin function on Ω is a Morse function, then for small ε the equation (⁎) has a unique solution, which is also nondegenerate. As for non-convex domain, we also obtain exact number of
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Parabolic automorphisms of hyperkähler manifolds J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-09-19 Ekaterina Amerik, Misha Verbitsky
A parabolic automorphism of a hyperkähler manifold M is a holomorphic automorphism acting on H2(M) by a non-semisimple quasi-unipotent linear map. We prove that a parabolic automorphism which preserves a Lagrangian fibration acts on almost all fibers ergodically. The existence of an invariant Lagrangian fibration is automatic for manifolds satisfying the hyperkähler SYZ conjecture; this includes all
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A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions II: Asymptotic profiles of solutions and radial terrace solution J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-08-02 Yuki Kaneko, Hiroshi Matsuzawa, Yoshio Yamada
This paper is a continuation of our previous paper (Kaneko-Matsuzawa-Yamada, Discrete Contin. Dyn. Syst., 2022), where we have classified all large-time behaviors of radially symmetric solutions to a free boundary problem of reaction diffusion equation ut=Δu+f(u) with positive bistable nonlinearity f in high space dimensions. The positive bistable nonlinearity means that f(u)=0 has exactly two positive
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Non-Kähler Calabi-Yau geometry and pluriclosed flow J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-08-02 Mario Garcia-Fernandez, Joshua Jordan, Jeffrey Streets
Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-Kähler manifolds, and arise independently in mathematical physics. We reinterpret this condition in terms of the Hermitian-Einstein equation on an associated holomorphic Courant algebroid, and thus refer to solutions as Bismut Hermitian-Einstein. This implies
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Global maximal regularity for equations with degenerate weights J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-08-01 Anna Kh. Balci, Sun-Sig Byun, Lars Diening, Ho-Sik Lee
In this paper we are concerned with global maximal regularity estimates for elliptic equations with degenerate weights. We consider both the linear case and the non-linear case. We show that higher integrability of the gradients can be obtained by imposing a local small oscillation condition on the weight and a local small Lipschitz condition on the boundary of the domain. Our results are new in the
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Kähler-Einstein metrics and obstruction flatness of circle bundles J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-08-01 Peter Ebenfelt, Ming Xiao, Hang Xu
Obstruction flatness of a strongly pseudoconvex hypersurface Σ in a complex manifold refers to the property that any (local) Kähler-Einstein metric on the pseudoconvex side of Σ, complete up to Σ, has a potential −logu such that u is C∞-smooth up to Σ. In general, u has only a finite degree of smoothness up to Σ. In this paper, we study obstruction flatness of hypersurfaces Σ that arise as unit circle
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Asymptotic stability manifolds for solitons in the generalized Good Boussinesq equation J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-08-01 Christopher Maulén
We consider the generalized Good-Boussinesq model in one dimension, with power nonlinearity and data in the energy space H1×L2. This model has solitary waves with speeds −1
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The nonlinear (p,q)-Schrödinger equation with a general nonlinearity: Existence and concentration J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-08-01 Vincenzo Ambrosio
We investigate the following class of (p,q)-Laplacian problems:{−εpΔpv−εqΔqv+V(x)(|v|p−2v+|v|q−2v)=f(v) in RN,v∈W1,p(RN)∩W1,q(RN),v>0 in RN, where ε>0 is a small parameter, N≥3, 10 and V0:=infΛV
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On long time behavior of the focusing energy-critical NLS on Rd×T via semivirial-vanishing geometry J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-08-01 Yongming Luo
We study the focusing energy-critical NLS(NLS)i∂tu+Δx,yu=−|u|4d−1u on the waveguide manifold Rxd×Ty with d≥2. We reveal the somewhat counterintuitive phenomenon that despite the energy-criticality of the nonlinear potential, the long time dynamics of (NLS) are purely determined by the semivirial-vanishing geometry which possesses an energy-subcritical characteristic. As a starting point, we consider
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Holomorphic motions, dimension, area and quasiconformal mappings J. Math. Pures Appl. (IF 2.3) Pub Date : 2023-08-01 Aidan Fuhrer, Thomas Ransford, Malik Younsi
We describe the variation of the Minkowski, packing and Hausdorff dimensions of a set moving under a holomorphic motion, as well as the variation of its area. Our method provides a new, unified approach to various celebrated theorems about quasiconformal mappings, including the work of Astala on the distortion of area and dimension under quasiconformal mappings and the work of Smirnov on the dimension