样式： 排序： IF:  GO 导出 标记为已读

Erratum for “Global Identifiability of Differential Models” Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230922
Hoon Hong, Alexey Ovchinnikov, Gleb Pogudin, Chee YapWe are grateful to Peter Thompson for pointing out an error in [1, Lemma 3.5, p. 1848]. The original proof worked only under the assumption that θ ̂ $\hat{\theta }$ is a vector of constants. However, some of the components of θ ̂ $\hat{\bm{\theta }}$ could be the states of the dynamic under consideration, and the lemma was used in such a setup (i.e., with θ ̂ $\hat{\bm{\theta }}$ involving states)

Discrete honeycombs, rational edges, and edge states Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230922
Charles L. Fefferman, Sonia Fliss, Michael I. WeinsteinConsider the tight binding model of graphene, sharply terminated along an edge l parallel to a direction of translational symmetry of the underlying period lattice. We classify such edges l into those of “zigzag type” and those of “armchair type”, generalizing the classical zigzag and armchair edges. We prove that zero energy / flat band edge states arise for edges of zigzag type, but never for those

An upper Minkowski dimension estimate for the interior singular set of area minimizing currents Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230918
Anna SkorobogatovaWe show that for an area minimizing mdimensional integral current T of codimension at least two inside a sufficiently regular Riemannian manifold, the upper Minkowski dimension of the interior singular set is at most m − 2 $m2$ . This provides a strengthening of the existing ( m − 2 ) $(m2)$ dimensional Hausdorff dimension bound due to Almgren and De Lellis & Spadaro. As a byproduct of the proof

Logarithmic cotangent bundles, ChernMather classes, and the HuhSturmfels involution conjecture Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230915
Laurenţiu G. Maxim, Jose Israel Rodriguez, Botong Wang, Lei WuUsing compactifications in the logarithmic cotangent bundle, we obtain a formula for the Chern classes of the pushforward of Lagrangian cycles under an open embedding with normal crossing complement. This generalizes earlier results of Aluffi and WuZhou. The first application of our formula is a geometric description of ChernMather classes of an arbitrary very affine variety, generalizing earlier

Landscape complexity beyond invariance and the elastic manifold Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230914
Gérard Ben Arous, Paul Bourgade, Benjamin McKennaThis paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elastic system captures point configurations with selfinteractions in a random medium. We establish the simple versus glassy phase diagram in the model parameters, with these phases separated by a physical boundary known as

Phase diagram and topological expansion in the complex quartic random matrix model Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230914
Pavel Bleher, Roozbeh Gharakhloo, Kenneth TR McLaughlinWe use the Riemann–Hilbert approach, together with string and Toda equations, to study the topological expansion in the quartic random matrix model. The coefficients of the topological expansion are generating functions for the numbers Nj(g)$\mathcal {N}_j(g)$ of 4valent connected graphs with j vertices on a compact Riemann surface of genus g. We explicitly evaluate these numbers for Riemann surfaces

Global minimizers of a large class of anisotropic attractiverepulsive interaction energies in 2D Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230914
José A. Carrillo, Ruiwen ShuWe study a large family of Riesztype singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas whose supports are determined by ellipses under certain assumptions. More precisely, by parameterizing the strength of the anisotropic part we characterize the sharp range in which these explicit ellipsesupported configurations

Complex analytic dependence on the dielectric permittivity in ENZ materials: The photonic doping example Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230914
Robert V. Kohn, Raghavendra VenkatramanMotivated by the physics literature on “photonic doping” of scatterers made from “epsilonnearzero” (ENZ) materials, we consider how the scattering of timeharmonic TM electromagnetic waves by a cylindrical ENZ region Ω × R $\Omega \times \mathbb {R}$ is affected by the presence of a “dopant” D ⊂ Ω $D \subset \Omega$ in which the dielectric permittivity is not near zero. Mathematically, this reduces

Magnetic slowdown of topological edge states Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230912
Guillaume Bal, Simon Becker, Alexis DrouotWe study the propagation of wavepackets along curved interfaces between topological, magnetic materials. Our Hamiltonian is a massive Dirac operator with a magnetic potential. We construct semiclassical wavepackets propagating along the curved interface as adiabatic modulations of straight edge states under constant magnetic fields. While in the magneticfree case, the wavepackets propagate coherently

Thermodynamic limit of the first LeeYang zero Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230911
Jianping Jiang, Charles M. NewmanWe complete the verification of the 1952 Yang and Lee proposal that thermodynamic singularities are exactly the limits in R ${\mathbb {R}}$ of finitevolume singularities in C ${\mathbb {C}}$ . For the Ising model defined on a finite Λ ⊂ Z d $\Lambda \subset \mathbb {Z}^d$ at inverse temperature β ≥ 0 $\beta \ge 0$ and external field h, let α 1 ( Λ , β ) $\alpha _1(\Lambda ,\beta )$ be the modulus

Compressive phase retrieval: Optimal sample complexity with deep generative priors Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230911
Paul Hand, Oscar Leong, Vladislav VoroninskiAdvances in compressive sensing (CS) provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with potentially fundamental sample complexity bottlenecks. In particular, tractable algorithms for compressive phase retrieval with sparsity priors have not been able

A scaling limit of the parabolic Anderson model with exclusion interaction Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230910
Dirk Erhard, Martin HairerWe consider the (discrete) parabolic Anderson model ∂ u ( t , x ) / ∂ t = Δ u ( t , x ) + ξ t ( x ) u ( t , x ) $\partial u(t,x)/\partial t=\Delta u(t,x) +\xi _t(x) u(t,x)$ , t ≥ 0 $t\ge 0$ , x ∈ Z d $x\in \mathbb {Z}^d$ , where the ξfield is R $\mathbb {R}$ valued and plays the role of a dynamic random environment, and Δ is the discrete Laplacian. We focus on the case in which ξ is given by a properly

Fermi isospectrality for discrete periodic Schrödinger operators Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230910
Wencai LiuLet Γ = q 1 Z ⊕ q 2 Z ⊕ … ⊕ q d Z $\Gamma =q_1\mathbb {Z}\oplus q_2 \mathbb {Z}\oplus \ldots \oplus q_d\mathbb {Z}$ , where q l ∈ Z + $q_l\in \mathbb {Z}_+$ , l = 1 , 2 , … , d $l=1,2,\ldots ,d$ , are pairwise coprime. Let Δ + V $\Delta +V$ be the discrete Schrödinger operator, where Δ is the discrete Laplacian on Z d $\mathbb {Z}^d$ and the potential V : Z d → C $V:\mathbb {Z}^d\rightarrow \mathbb

Critical local wellposedness for the fully nonlinear Peskin problem Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230908
Stephen Cameron, Robert M. StrainWe study the problem where a onedimensional elastic string is immersed in a twodimensional steady Stokes fluid. This is known as the Stokes immersed boundary problem and also as the Peskin problem. We consider the case with equal viscosities and with a fully nonlinear tension law; this model has been called the fully nonlinear Peskin problem. In this case we prove local in time wellposedness for

Pure gravity traveling quasiperiodic water waves with constant vorticity Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230909
Massimiliano Berti, Luca Franzoi, Alberto MasperoWe prove the existence of small amplitude time quasiperiodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a NashMoser implicit function iterative scheme we construct traveling nonlinear waves which pass through each other slightly deforming and retaining forever a quasiperiodic

Convergence of the selfdual U(1)Yang–Mills–Higgs energies to the (n−2)$(n2)$area functional Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230907
Davide Parise, Alessandro Pigati, Daniel SternGiven a hermitian line bundle L → M $L\rightarrow M$ on a closed Riemannian manifold ( M n , g ) $(M^n,g)$ , the selfdual Yang–Mills–Higgs energies are a natural family of functionals

C2,α$C^{2,\alpha }$ regularity of free boundaries in optimal transportation Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230907
Shibing Chen, Jiakun Liu, XuJia WangThe regularity of the free boundary in optimal transportation is equivalent to that of the potential function along the free boundary. By establishing new geometric estimates of the free boundary and studying the second boundary value problem of the MongeAmpère equation, we obtain the C 2 , α $C^{2,\alpha }$ regularity of the potential function as well as that of the free boundary, thereby resolve

Constrained deformations of positive scalar curvature metrics, II Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230907
Alessandro Carlotto, Chao LiWe prove that various spaces of constrained positive scalar curvature metrics on compact threemanifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean curvature of the boundary, and our treatment includes both the meanconvex and the minimal case. We then discuss the implications of these results on the topology

Prescribed curvature measure problem in hyperbolic space Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230907
Fengrui YangThe problem of the prescribed curvature measure is one of the important problems in differential geometry and nonlinear partial differential equations. In this paper, we consider the prescribed curvature measure problem in the hyperbolic space. We obtain the existence of starshaped kconvex bodies with prescribed (nk)th curvature measures ( k < n ) $(k

Free boundary partial regularity in the thin obstacle problem Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230905
Federico Franceschini, Joaquim SerraFor the thin obstacle problem in R n $\mathbb {R}^n$ , n ≥ 2 $n\ge 2$ , we prove that at all free boundary points, with the exception of a ( n − 3 ) $(n3)$ dimensional set, the solution differs from its blowup by higher order corrections. This expansion entails a C1, 1type free boundary regularity result, up to a codimension 3 set.

Existence of multidimensional contact discontinuities for the ideal compressible magnetohydrodynamics Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230905
Yanjin Wang, Zhouping XinWe establish the local existence and uniqueness of multidimensional contact discontinuities for the ideal compressible magnetohydrodynamics (MHD) in Sobolev spaces, which are most typical interfacial waves for astrophysical plasmas and prototypical fundamental waves for hyperbolic systems of conservation laws. Such waves are characteristic discontinuities for which there is no flow across the discontinuity

Hearing the shape of ancient noncollapsed flows in R4$\mathbb {R}^{4}$ Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230905
Wenkui Du, Robert HaslhoferWe consider ancient noncollapsed mean curvature flows in R 4 $\mathbb {R}^4$ whose tangent flow at − ∞ $\infty$ is a bubblesheet. We carry out a fine spectral analysis for the bubblesheet function u that measures the deviation of the renormalized flow from the round cylinder R 2 × S 1 ( 2 ) $\mathbb {R}^2 \times S^1(\sqrt {2})$ and prove that for τ → − ∞ $\tau \rightarrow \infty$ we have the fine

On the MaxwellBloch system in the sharpline limit without solitons Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230821
Sitai Li, Peter D. MillerWe study the (characteristic) Cauchy problem for the MaxwellBloch equations of lightmatter interaction via asymptotics, under assumptions that prevent the generation of solitons. Our analysis clarifies some features of the sense in which physicallymotivated initialboundary conditions are satisfied. In particular, we present a proper RiemannHilbert problem that generates the unique causal solution

A generalization of Geroch's conjecture Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230812
Simon Brendle, Sven Hirsch, Florian JohneThe Theorem of Bonnet–Myers implies that manifolds with topology M n − 1 × S 1 $M^{n1} \times \mathbb {S}^1$ do not admit a metric of positive Ricci curvature, while the resolution of Geroch's conjecture implies that the torus T n $\mathbb {T}^n$ does not admit a metric of positive scalar curvature. In this work we introduce a new notion of curvature interpolating between Ricci and scalar curvature

Decay of scalar curvature on uniformly contractible manifolds with finite asymptotic dimension Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230802
Jinmin Wang, Zhizhang Xie, Guoliang YuGromov proved a quadratic decay inequality of scalar curvature for a class of complete manifolds. In this paper, we prove that for any uniformly contractible manifold with finite asymptotic dimension, its scalar curvature decays to zero at a rate depending only on the contractibility radius of the manifold and the diameter control of the asymptotic dimension. We construct examples of uniformly contractible

Stability of the tangent bundle through conifold transitions Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230728
Tristan Collins, Sebastien Picard, ShingTung YauLet X be a compact, Kähler, CalabiYau threefold and suppose X ↦ X ̲ ⇝ X t $X\mapsto \underline{X}\leadsto X_t$ , for t ∈ Δ $t\in \Delta$ , is a conifold transition obtained by contracting finitely many disjoint ( − 1 , − 1 ) $(1,1)$ curves in X and then smoothing the resulting ordinary double point singularities. We show that, for  t  ≪ 1 $t\ll 1$ sufficiently small, the tangent bundle T 1

Rigorous datadriven computation of spectral properties of Koopman operators for dynamical systems Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230727
Matthew J. Colbrook, Alex TownsendKoopman operators are infinitedimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. However, Koopman operators can have continuous spectra and infinitedimensional invariant subspaces, making computing their spectral information a considerable challenge. This paper describes datadriven algorithms with rigorous

Integrability of Einstein deformations and desingularizations Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230726
Tristan OzuchWe study the question of the integrability of Einstein deformations and relate it to the question of the desingularization of Einstein metrics. Our main application is a negative answer to the longstanding question of whether or not every Einstein 4orbifold (which is an Einstein metric space in a synthetic sense) is limit of smooth Einstein 4manifolds. We more precisely show that spherical and hyperbolic

Shattering versus metastability in spin glasses Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230725
Gérard Ben Arous, Aukosh JagannathOur goal in this work is to better understand the relationship between replica symmetry breaking, shattering, and metastability. To this end, we study the static and dynamic behaviour of spherical pure pspin glasses above the replica symmetry breaking temperature T s $T_{s}$ . In this regime, we find that there are at least two distinct temperatures related to nontrivial behaviour. First we prove

Stability of Hill's spherical vortex Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230724
Kyudong ChoiWe study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit solution of the threedimensional incompressible Euler equations. The flow is axisymmetric with no swirl, the vortex core is simply a ball sliding on the axis of symmetry with a constant speed, and the vorticity in the core is proportional to the distance from the symmetry axis. We use the variational setting

Long range order for random field Ising and Potts models Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230722
Jian Ding, Zijie ZhuangWe present a new and simple proof for the classic results of Imbrie (1985) and Bricmont–Kupiainen (1988) that for the random field Ising model in dimension three and above there is long range order at low temperatures with presence of weak disorder. With the same method, we obtain a couple of new results: (1) we prove that long range order exists for the random field Potts model at low temperatures

Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230721
Alessio Figalli, Yi RuYa ZhangWe consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is wellknown that:

Contact points with integer frequencies in the thin obstacle problem Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230721
Ovidiu Savin, Hui YuFor the thin obstacle problem, we develop a unified approach that leads to rates of convergence to blowup profiles at contact points with integer frequencies. For these points, we also obtain a stratification result.

Large deviations principle for the cubic NLS equation Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230721
Miguel Angel Garrido, Ricardo Grande, Kristin M. Kurianski, Gigliola StaffilaniIn this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schrödinger equation on the torus in a weakly nonlinear setting. This equation has been used as a model to numerically study the formation of rogue waves in deep sea. Our results are twofold: first, we introduce a notion of criticality and prove a Large Deviations Principle (LDP) for the subcritical and critical

Regularity for convex viscosity solutions of special Lagrangian equation Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230721
Jingyi Chen, Ravi Shankar, Yu YuanWe establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain.

Singularities almost always scatter: Regularity results for nonscattering inhomogeneities Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230717
Fioralba Cakoni, Michael S. VogeliusIn this paper we examine necessary conditions for an inhomogeneity to be nonscattering, or equivalently, by negation, sufficient conditions for it to be scattering. These conditions are formulated in terms of the regularity of the boundary of the inhomogeneity. We examine broad classes of incident waves in both two and three dimensions. Our analysis is greatly influenced by the analysis carried out

Shorttime existence for the network flow Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230713
Jorge Lira, Rafe Mazzeo, Alessandra Pluda, Mariel SáezThis paper contains a new proof of the shorttime existence for the flow by curvature of a network of curves in the plane. Appearing initially in metallurgy and as a model for the evolution of grain boundaries, this flow was later treated by Brakke using varifold methods. There is good reason to treat this problem by a direct PDE approach, but doing so requires one to deal with the singular nature

Global wellposedness for the onephase Muskat problem Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230711
Hongjie Dong, Francisco Gancedo, Huy Q. NguyenThe free boundary problem for a twodimensional fluid permeating a porous medium is studied. This is known as the onephase Muskat problem and is mathematically equivalent to the vertical HeleShaw problem driven by gravity force. We prove that if the initial free boundary is the graph of a periodic Lipschitz function, then there exists a globalintime Lipschitz solution in the strong L t ∞ L x 2

Longtime correlations for a hardsphere gas at equilibrium Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230709
Thierry Bodineau, Isabelle Gallagher, Laure SaintRaymond, Sergio SimonellaIt has been known since Lanford that the dynamics of a hardsphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to equilibrium. In this paper, we introduce a weak convergence method coupled with a sampling argument to prove that the covariance of the fluctuation field around equilibrium

Generalization of wavingplate theory to multiple interacting swimmers Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230707
Peter J. Baddoo, Nicholas J. Moore, Anand U. Oza, Darren G. CrowdyEarly research in aerodynamics and biological propulsion was dramatically advanced by the analytical solutions of Theodorsen, von Kármán, Wu and others. While these classical solutions apply only to isolated swimmers, the flow interactions between multiple swimmers are relevant to many practical applications, including the schooling and flocking of animal collectives. In this work, we derive a class

Reflective prolatespheroidal operators and the adelic Grassmannian Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230704
W. Riley Casper, F. Alberto Grünbaum, Milen Yakimov, Ignacio ZurriánBeginning with the work of Landau, Pollak and Slepian in the 1960s on timeband limiting, commuting pairs of integral and differential operators have played a key role in signal processing, random matrix theory, and integrable systems. Previously, such pairs were constructed by ad hoc methods, which essentially worked because a commuting operator of low order could be found by a direct calculation

Detecting the birth and death of finitetime coherent sets Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230703
Gary Froyland, Péter KoltaiFinitetime coherent sets (FTCSs) are distinguished regions of phase space that resist mixing with the surrounding space for some finite period of time; physical manifestations include eddies and vortices in the ocean and atmosphere, respectively. The boundaries of FTCSs are examples of Lagrangian coherent structures (LCSs). The selection of the time duration over which FTCS and LCS computations are

Nonlinear inviscid damping and shearbuoyancy instability in the twodimensional Boussinesq equations Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230703
Jacob Bedrossian, Roberta Bianchini, Michele Coti Zelati, Michele DolceWe investigate the longtime properties of the twodimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ε. Under the classical MilesHoward stability condition on the Richardson number, we prove that the system experiences a shearbuoyancy instability: the density variation and velocity undergo an O ( t − 1 / 2 ) $O(t^{1/2})$ inviscid

Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230703
SeungYeop Lee, Meng YangWe consider the orthogonal polynomial pn(z) with respect to the planar measure supported on the whole complex plane

On the stabilizing effect of rotation in the 3d Euler equations Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230701
Yan Guo, Chunyan Huang, Benoit Pausader, Klaus WidmayerWhile it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d rotating Euler equations in R 3 $\mathbb {R}^3$ with a fixed speed of rotation. We show that for any M > 0 $\mathcal {M}> 0$ , axisymmetric initial data of sufficiently

Polynomialtime universality and limitations of deep learning Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230630
Emmanuel Abbe, Colin SandonThe goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is polytime universal: any function distribution that can be learned from samples in polytime can also be learned by a polysize neural net trained by SGD with

Giant component for the supercritical levelset percolation of the Gaussian free field on regular expander graphs Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230628
Jiří ČernýWe consider the zeroaverage Gaussian free field on a certain class of finite dregular graphs for fixed d ≥ 3 $d\ge 3$ . This class includes dregular expanders of large girth and typical realisations of random dregular graphs. We show that the level set of the zeroaverage Gaussian free field above level h has a giant component in the whole supercritical phase, that is for all h < h ★ $h

Existence of constant mean curvature 2Spheres in Riemannian 3spheres Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230628
Da Rong Cheng, Xin ZhouWe prove the existence of branched immersed constant mean curvature (CMC) 2spheres in an arbitrary Riemannian 3sphere for almost every prescribed mean curvature, and moreover for all prescribed mean curvatures when the 3sphere is positively curved. To achieve this, we develop a minmax scheme for a weighted Dirichlet energy functional. There are three main ingredients in our approach: a biharmonic

Compressible NavierStokes equations with ripped density Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230628
Raphaël Danchin, Piotr BogusŁaw MuchaWe are concerned with the Cauchy problem for the twodimensional compressible NavierStokes equations supplemented with general H1 initial velocity and bounded initial density not necessarily strictly positive: it may be the characteristic function of any set, for instance. In the perfect gas case, we establish globalintime existence and uniqueness, provided the volume (bulk) viscosity coefficient

The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230627
Elliot Blackstone, Christophe Charlier, Jonatan LenellsThe Bessel process models the local eigenvalue statistics near 0 of certain large positive definite matrices. In this work, we consider the probability

Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230623
Manuela Girotti, Tamara Grava, Robert Jenkins, Ken TR McLaughlin, Alexander MinakovWe analyse the case of a dense modified Korteweg–de Vries (mKdV) soliton gas and its large time behaviour in the presence of a single trial soliton. We show that the solution can be expressed in terms of Fredholm determinants as well as in terms of a Riemann–Hilbert problem. We then show that the solution can be decomposed as the sum of the background gas solution (a modulated elliptic wave), plus

Validity of steady Prandtl layer expansions Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230613
Yan Guo, Sameer IyerLet the viscosity ε → 0 $\varepsilon \rightarrow 0$ for the 2D steady NavierStokes equations in the region 0 ≤ x ≤ L $0\le x\le L$ and 0 ≤ y < ∞ $0\le y<\infty$ with no slip boundary conditions at y = 0 $y=0$ . For L < < 1 $L<<1$ , we justify the validity of the steady Prandtl layer expansion for scaled Prandtl layers, including the celebrated Blasius boundary layer. Our uniform estimates in ε are

The stationary AKPZ equation: Logarithmic superdiffusivity Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230605
Giuseppe Cannizzaro, Dirk Erhard, Fabio ToninelliWe study the twodimensional Anisotropic KPZ equation (AKPZ) formally given by

Fluctuation exponents of the KPZ equation on a large torus Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230605
Alexander Dunlap, Yu Gu, Tomasz KomorowskiWe study the onedimensional KPZ equation on a large torus, started at equilibrium. The main results are optimal variance bounds in the superrelaxation regime and part of the relaxation regime.

Variational methods for a singular SPDE yielding the universality of the magnetization ripple Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230602
Radu Ignat, Felix Otto, Tobias Ried, Pavlos TsatsoulisThe magnetization ripple is a microstructure formed in thin ferromagnetic films. It can be described by minimizers of a nonconvex energy functional leading to a nonlocal and nonlinear elliptic SPDE in two dimensions driven by white noise, which is singular. We address the universal character of the magnetization ripple using variational methods based on Γconvergence. Due to the infinite energy of

LongTime Instability of the Couette Flow in Low Gevrey Spaces Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230424
Yu Deng, Nader MasmoudiWe prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2. A big novelty is that this critical space is due to an instability mechanism which is

Vortex Filament Solutions of the NavierStokes Equations Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230324
Jacob Bedrossian, Pierre Germain, Benjamin HarropGriffithsWe consider solutions of the NavierStokes equations in 3d with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergencefree vectorvalued measure of arbitrary mass supported on a smooth curve. First, we prove global wellposedness for perturbations of the Oseen vortex column in scalingcritical spaces. Second, we prove local wellposedness (in a sense

A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230130
Angelo Alvino, Carlo Nitsch, Cristina TrombettiComparison results of Talenti type for elliptic problems with Dirichlet boundary conditions have been widely investigated in recent decades. In this paper, we deal with Robin boundary conditions. Surprisingly, contrary to the Dirichlet case, Robin boundary conditions make the comparison sensitive to the dimension, and while the planar case seems to be completely settled, in higher dimensions some open

Sigma Delta Quantization for Images Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20230118
He Lyu, Rongrong WangIn signal quantization, it is wellknown that introducing adaptivity to quantization schemes can improve their stability and accuracy in quantizing bandlimited signals. However, adaptive quantization has only been designed for onedimensional signals. The contribution of this paper is twofold: (i) we propose the first family of twodimensional adaptive quantization schemes that maintain the same mathematical

Limit Set of Branching Random Walks on Hyperbolic Groups Comm. Pure Appl. Math. (IF 3.0) Pub Date : 20221208
Vladas Sidoravicius, Longmin Wang, Kainan XiangLet Γ be a nonelementary hyperbolic group with a word metric d and ∂Γ its hyperbolic boundary equipped with a visual metric d a for some parameter a > 1 . Fix a superexponential symmetric probability μ on Γ whose support generates Γ as a semigroup, and denote by ρ the spectral radius of the random walk Y on Γ with step distribution μ. Let ν be a probability on 1,2,3 , … with mean λ = ∑ k = 1 ∞ kν k