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Phase-Field Approximation of a Vectorial, Geometrically Nonlinear Cohesive Fracture Energy Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-03-16 Sergio Conti, Matteo Focardi, Flaviana Iurlano
We consider a family of vectorial models for cohesive fracture, which may incorporate \(\textrm{SO}(n)\)-invariance. The deformation belongs to the space of generalized functions of bounded variation and the energy contains an (elastic) volume energy, an opening-dependent jump energy concentrated on the fractured surface, and a Cantor part representing diffuse damage. We show that this type of functional
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Well-Posedness of the Dean–Kawasaki and the Nonlinear Dawson–Watanabe Equation with Correlated Noise Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-03-11
Abstract In this paper we prove the well-posedness of the generalized Dean–Kawasaki equation driven by noise that is white in time and colored in space. The results treat diffusion coefficients that are only locally \({1}/{2}\) -Hölder continuous, including the square root. This solves several open problems, including the well-posedness of the Dean–Kawasaki equation and the nonlinear Dawson–Watanabe
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A Counterexample to the Theorem of Laplace–Lagrange on the Stability of Semimajor Axes Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-02-21 Andrew Clarke, Jacques Fejoz, Marcel Guardia
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Existence of Optimal Shapes in Parabolic Bilinear Optimal Control Problems Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-02-15 Idriss Mazari-Fouquer
The aim of this paper is to prove the existence of optimal shapes in bilinear parabolic optimal control problems. We consider a parabolic equation \(\partial _tu_m-\Delta u_m=f(t,x,u_m)+mu_m\). The set of admissible controls is given by \(A=\{m\in L^\infty \,, m_-\leqq m\leqq m_+{\text { almost everywhere, }}\int _\Omega m(t,\cdot )=V_1(t)\}\), where \(m_\pm =m_\pm (t,x)\) are two reference functions
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The Existence of Meissner Solutions to the Full Ginzburg–Landau System in Three Dimensions Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-02-14 Xingbin Pan, Xingfei Xiang
In this paper we establish the existence of the locally stable Meissner solutions of the three dimensional full Ginzburg–Landau system of superconductivity.
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Front Selection in Reaction–Diffusion Systems via Diffusive Normal Forms Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-02-13 Montie Avery
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The Loewner Energy via the Renormalised Energy of Moving Frames Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-02-12 Alexis Michelat, Yilin Wang
We obtain a new formula for the Loewner energy of Jordan curves on the sphere, which is a Kähler potential for the essentially unique Kähler metric on the Weil–Petersson universal Teichmüller space, as the renormalised energy of moving frames on the two domains of the sphere delimited by the given curve.
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Gradient Decay in the Boltzmann Theory of Non-isothermal Boundary Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-02-06
Abstract We consider the Boltzmann equation in a convex domain with a non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belonging to \(W^{1,p}_x\) for any \(p<3\) . We prove that the unsteady solution converges to the steady solution in the same Sobolev space exponentially quickly as \(t \rightarrow \infty \) .
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The $$L^p$$ Teichmüller Theory: Existence and Regularity of Critical Points Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-02-02 Gaven Martin, Cong Yao
We study minimisers of the p-conformal energy functionals, $$\begin{aligned} \textsf{E}_p(f):=\int _{\mathbb {D}}{\mathbb {K}}^p(z,f)\,\text {d}z,\quad f|_{\mathbb {S}}=f_0|_{\mathbb {S}}, \end{aligned}$$ defined for self mappings \(f:{\mathbb {D}}\rightarrow {\mathbb {D}}\) with finite distortion and prescribed boundary values \(f_0\). Here $$\begin{aligned} {\mathbb {K}}(z,f) = \frac{\Vert Df(z)\Vert
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A Limit of Nonplanar 5-Body Central Configurations is Nonplanar Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-31 Alain Albouy, Antonio Carlos Fernandes
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Intermittency and Lower Dimensional Dissipation in Incompressible Fluids Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-25 Luigi De Rosa, Philip Isett
In the context of incompressible fluids, the observation that turbulent singular structures fail to be space filling is known as “intermittency”, and it has strong experimental foundations. Consequently, as first pointed out by Landau, real turbulent flows do not satisfy the central assumptions of homogeneity and self-similarity in the K41 theory, and the K41 prediction of structure function exponents
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Local Well-Posedness of the Skew Mean Curvature Flow for Small Data in $$d\geqq 2$$ Dimensions Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-25 Jiaxi Huang, Daniel Tataru
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The BPHZ Theorem for Regularity Structures via the Spectral Gap Inequality Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-23 Martin Hairer, Rhys Steele
We provide a relatively compact proof of the BPHZ theorem for regularity structures of decorated trees in the case where the driving noise satisfies a suitable spectral gap property, as in the Gaussian case. This is inspired by the recent work (Linares et al. in A diagram-free approach to the stochastic estimates in regularity structures, 2021. arXiv:2112.10739) in the multi-index setting, but our
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Stability and Cascades for the Kolmogorov–Zakharov Spectrum of Wave Turbulence Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-23 Charles Collot, Helge Dietert, Pierre Germain
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Weak Solutions of Mullins–Sekerka Flow as a Hilbert Space Gradient Flow Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-23
Abstract We propose a novel weak solution theory for the Mullins–Sekerka equation in dimensions \(d=2\) and 3, primarily motivated from a gradient flow perspective. Previous existence results on weak solutions due to Luckhaus and Sturzenhecker (Calc. Var. PDE 3, 1995) or Röger (SIAM J. Math. Anal. 37, 2005) left open the inclusion of both a sharp energy dissipation principle and a weak formulation
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Microscopic Derivation of a Traffic Flow Model with a Bifurcation Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-19 P. Cardaliaguet, N. Forcadel
The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random parameters are used as a statistical description of the road taken by a vehicle and its law of motion. The limit model is a deterministic and scalar Hamilton–Jacobi
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Traveling Wave Solutions to the One-Phase Muskat Problem: Existence and Stability Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-18 Huy Q. Nguyen, Ian Tice
We study the Muskat problem for one fluid in an arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitational field, the fluid is acted upon by a generic force field in the bulk and an external pressure on the free boundary, both of which are posited to be in traveling wave form. We prove that, for sufficiently small force
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Stable Singularity Formation for the Keller–Segel System in Three Dimensions Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2024-01-05 Irfan Glogić, Birgit Schörkhuber
We consider the parabolic–elliptic Keller–Segel system in dimensions \(d \geqq 3\), which is the mass supercritical case. This system is known to exhibit rich dynamical behavior including singularity formation via self-similar solutions. An explicit example was found more than two decades ago by Brenner et al. (Nonlinearity 12(4):1071–1098, 1999), and is conjectured to be nonlinearly radially stable
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Localized Big Bang Stability for the Einstein-Scalar Field Equations Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-12-08 Florian Beyer, Todd A. Oliynyk
We prove the nonlinear stability in the contracting direction of Friedmann–Lemaître–Robertson–Walker (FLRW) solutions to the Einstein-scalar field equations in \(n\ge 3\) spacetime dimensions that are defined on spacetime manifolds of the form \((0,t_0]\times \mathbb {T}{}^{n-1}\), \(t_0>0\). Stability is established under the assumption that the initial data is synchronized, which means that on the
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Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-12-07 Vesa Julin, Joonas Niinikoski
We consider the flat flow solution, obtained via a discrete minimizing movement scheme, to the volume preserving mean curvature flow starting from \(C^{1,1}\)-regular set. We prove the consistency principle, which states that (any) flat flow solution agrees with the classical solution as long as the latter exists. In particular the flat flow solution is unique and smooth up to the first singular time
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Relaxation Approximation and Asymptotic Stability of Stratified Solutions to the IPM Equation Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-12-08 Roberta Bianchini, Timothée Crin-Barat, Marius Paicu
We prove the nonlinear asymptotic stability of stably stratified solutions to the Incompressible Porous Media equation (IPM) for initial perturbations in \(\dot{H}^{1-\tau }(\mathbb {R}^2) \cap \dot{H}^s(\mathbb {R}^2)\) with \(s > 3\) and for any \(0< \tau <1\). Such a result improves upon the existing literature, where the asymptotic stability is proved for initial perturbations belonging at least
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Fine Properties of Geodesics and Geodesic $$\lambda $$ -Convexity for the Hellinger–Kantorovich Distance Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-11-29 Matthias Liero, Alexander Mielke, Giuseppe Savaré
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Functions with Bounded Hessian–Schatten Variation: Density, Variational, and Extremality Properties Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-11-20 Luigi Ambrosio, Camillo Brena, Sergio Conti
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Two-Dimensional Ferronematics, Canonical Harmonic Maps and Minimal Connections Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-11-17 Giacomo Canevari, Apala Majumdar, Bianca Stroffolini, Yiwei Wang
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Weak and Strong Versions of the Kolmogorov 4/5-Law for Stochastic Burgers Equation Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-11-12 Peng Gao, Sergei Kuksin
For solutions of the space-periodic stochastic 1d Burgers equation we establish two versions of the Kolmogorov 4/5-law; this provides an asymptotic expansion for the third moment of increments of turbulent velocity fields. We also prove for this equation an analogy of the Landau objection to possible universality of Kolmogorov’s theory of turbulence, and show that the third moment is the only one which
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Free Boundary Minimal Annuli Immersed in the Unit Ball Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-11-10 Isabel Fernández, Laurent Hauswirth, Pablo Mira
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Beyond the Classical Cauchy–Born Rule Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-11-07 Andrea Braides, Andrea Causin, Margherita Solci, Lev Truskinovsky
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A Remark on the Uniqueness of Solutions to Hyperbolic Conservation Laws Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-10-30 Alberto Bressan, Camillo De Lellis
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Epsilon-Regularity for Griffith Almost-Minimizers in Any Dimension Under a Separating Condition Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-10-13 Camille Labourie, Antoine Lemenant
In this paper we prove that if (u, K) is an almost-minimizer of the Griffith functional and K is \(\varepsilon \)-close to a plane in some ball \(B\subset {\mathbb {R}}^N\) while separating the ball B in two big parts, then K is \(C^{1,\alpha }\) in a slightly smaller ball. Our result contains and generalizes the 2 dimensional result of Babadjian et al. (J Eur Math Soc 24(7):2443–2492, 2022), with
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The Yang–Mills–Higgs Functional on Complex Line Bundles: $$\Gamma $$ -Convergence and the London Equation Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-10-09 Giacomo Canevari, Federico Luigi Dipasquale, Giandomenico Orlandi
We consider the Abelian Yang–Mills–Higgs functional, in the non-self dual scaling, on a complex line bundle over a closed Riemannian manifold of dimension \(n\ge 3\). This functional is the natural generalisation of the Ginzburg–Landau model for superconductivity to the non-Euclidean setting. We prove a \(\Gamma \)-convergence result, in the strongly repulsive limit, on the functional rescaled by the
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Long-time asymptotics for coagulation equations with injection that do not have stationary solutions Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-10-06 Iulia Cristian, Marina A. Ferreira, Eugenia Franco, Juan J. L. Velázquez
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Stability of the Nonlinear Milne Problem for Radiative Heat Transfer System Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-09-27 Mohamed Ghattassi, Xiaokai Huo, Nader Masmoudi
This paper focuses on the nonlinear Milne problem of the radiative heat transfer system on the half-space. The nonlinear model is described by a second order ODE for temperature coupled to transport equation for radiative intensity. The nonlinearity of the fourth power Stefan–Boltzmann law of black body radiation, brings additional difficulty in mathematical analysis, compared to the well-developed
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Gaussian Fluctuations for Interacting Particle Systems with Singular Kernels Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-09-27 Zhenfu Wang, Xianliang Zhao, Rongchan Zhu
We consider the asymptotic behaviour of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized Ornstein–Uhlenbeck process. Our result considerably extends classical results to singular kernels, including the Biot–Savart law. The result applies to the point vortex
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Exterior Stability of Minkowski Space in Generalized Harmonic Gauge Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-09-24 Peter Hintz
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Free Boundary Problem for a Gas Bubble in a Liquid, and Exponential Stability of the Manifold of Spherically Symmetric Equilibria Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-09-25 Chen-Chih Lai, Michael I. Weinstein
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Global Bifurcation and Highest Waves on Water of Finite Depth Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-09-20 Vladimir Kozlov, Evgeniy Lokharu
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On the Norm Equivalence of Lyapunov Exponents for Regularizing Linear Evolution Equations Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-09-16 Alex Blumenthal, Sam Punshon-Smith
We consider the top Lyapunov exponent associated to a dissipative linear evolution equation posed on a separable Hilbert or Banach space. In many applications in partial differential equations, such equations are often posed on a scale of nonequivalent spaces mitigating, e.g., integrability (\(L^p\)) or differentiability (\(W^{s, p}\)). In contrast to finite dimensions, the Lyapunov exponent could
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On Magnetic Inhibition Theory in 3D Non-resistive Magnetohydrodynamic Fluids: Global Existence of Large Solutions Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-09-13 Fei Jiang, Song Jiang
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The Insulated Conductivity Problem with p-Laplacian Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-30 Hongjie Dong, Zhuolun Yang, Hanye Zhu
We study the insulated conductivity problem with closely spaced insulators embedded in a homogeneous matrix where the current-electric field relation is the power law \(J = |E|^{p-2}E\). The gradient of solutions may blow up as \(\varepsilon \), the distance between insulators, approaches to 0. We prove an upper bound of the gradient to be of order \(\varepsilon ^{-\alpha }\), where \(\alpha = 1/2\)
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Optimal Estimates on the Propagation of Reactions with Fractional Diffusion Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-28 Yuming Paul Zhang, Andrej Zlatoš
We study the reaction-fractional-diffusion equation \(u_t+(-\Delta )^{s} u=f(u)\) with ignition and monostable reactions f, and \(s\in (0,1)\). We obtain the first optimal bounds on the propagation of front-like solutions in the cases where no traveling fronts exist. Our results cover most of these cases, and also apply to propagation from localized initial data.
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Homogenization and Phase Separation with Space Dependent Wells: The Subcritical Case Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-29 Riccardo Cristoferi, Irene Fonseca, Likhit Ganedi
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On the Linearized System of Equations for the Condensate-Normal Fluid Interaction Near the Critical Temperature Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-25 M. Escobedo
The Cauchy problem for the linearization around one of its equilibria of a non linear system of equations, arising in the kinetic theory of a condensed gas of bosons near the critical temperature, is solved for radially symmetric initial data. As time tends to infinity, the solutions are proved to converge to an equilibrium of the same linear system, determined by the conservation of total mass and
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Benjamin–Feir Instability of Stokes Waves in Finite Depth Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-25 Massimiliano Berti, Alberto Maspero, Paolo Ventura
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On Explicit $$L^2$$ -Convergence Rate Estimate for Underdamped Langevin Dynamics Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-24 Yu Cao, Jianfeng Lu, Lihan Wang
We provide a refined explicit estimate of the exponential decay rate of underdamped Langevin dynamics in the \(L^2\) distance, based on a framework developed in Albritton et al. (Variational methods for the kinetic Fokker–Planck equation, arXiv arXiv:1902.04037, 2019). To achieve this, we first prove a Poincaré-type inequality with a Gibbs measure in space and a Gaussian measure in momentum. Our estimate
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Anisotropic Regularity of the Free-Boundary Problem in Compressible Ideal Magnetohydrodynamics Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-24 Hans Lindblad, Junyan Zhang
We consider that 3D free-boundary compressible ideal magnetohydrodynamic (MHD) system under the Rayleigh-Taylor sign condition. This describes the motion of a free-surface perfect conducting fluid in an electro-magnetic field. A local existence and uniqueness result was recently proved by Trakhinin and Wang (Arch Ration Mech Anal 239(2):1131–1176, 2021) by using Nash–Moser iteration. However, that
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Quantitative Steepness, Semi-FKPP Reactions, and Pushmi-Pullyu Fronts Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-21 Jing An, Christopher Henderson, Lenya Ryzhik
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A Sharp Gradient Estimate and $$W^{2,q}$$ Regularity for the Prescribed Mean Curvature Equation in the Lorentz-Minkowski Space Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-21 Denis Bonheure, Alessandro Iacopetti
We consider the prescribed mean curvature equation for entire spacelike hypersurfaces in the Lorentz-Minkowski space, namely $$\begin{aligned} -{\text {div}}\left( \displaystyle \frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right) = \rho \quad \hbox {in }{\mathbb {R}}^N, \end{aligned}$$ where \(N\geqq 3\). We first prove a new gradient estimate for classical solutions with smooth data \(\rho \). As a consequence
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The Kinetic and Hydrodynamic Bohm Criteria for Plasma Sheath Formation Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-19 Masahiro Suzuki, Masahiro Takayama
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Regularity for Double Phase Problems at Nearly Linear Growth Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-18 Cristiana De Filippis, Giuseppe Mingione
Minima of functionals of the type $$\begin{aligned} w\mapsto \int _{\varOmega }\left[ |Dw|\log (1+|Dw|)+a(x)|Dw|^{q}\right] \, \textrm{d}x, \quad 0\le a(\cdot ) \in C^{0, \alpha }, \end{aligned}$$ with \(\varOmega \subset {\mathbb {R}}^n\), have locally Hölder continuous gradient provided \(1< q < 1+\alpha /n\).
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Uniqueness of Positive Vorticity Solutions to the 2d Euler Equations on Singular Domains Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-17 Zonglin Han, Andrej Zlatoš
We show that particle trajectories for positive vorticity solutions to the 2D Euler equations on fairly general bounded simply connected domains cannot reach the boundary in finite time. This includes domains with possibly nowhere \(C^1\) boundaries and having corners with arbitrary angles, and can fail without the sign hypothesis when the domain has large angle corners. Hence, positive vorticity solutions
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Linear Instability Analysis on Compressible Navier–Stokes Equations with Strong Boundary Layer Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-17 Tong Yang, Zhu Zhang
A classical problem in fluid mechanics concerns the stability and instability of different hydrodynamic patterns in various physical settings, particularly in the high Reynolds number limit of laminar flows with boundary layers. Despite extensive studies when the fluid is governed by incompressible Navier-Stokes equations, there are very few mathematical results on the compressible fluid. This paper
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Weak Limit of Homeomorphisms in $$W^{1,n-1}$$ and (INV) Condition Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-16 Anna Doležalová, Stanislav Hencl, Jan Malý
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Green’s Function and Pointwise Behavior of the One-Dimensional Vlasov–Maxwell–Boltzmann System Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-17 Hai-Liang Li, Tong Yang, Mingying Zhong
The pointwise space-time behavior of the Green’s function of the one-dimensional Vlasov–Maxwell–Boltzmann (VMB) system is studied in this paper. It is shown that the Green’s function consists of the macroscopic diffusive waves and Huygens waves with the speed \(\pm \sqrt{\frac{5}{3}}\) at low-frequency, the hyperbolic waves with the speed \(\pm 1\) at high-frequency, the singular kinetic and leading
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Time-Asymptotic Expansion with Pointwise Remainder Estimates for 1D Viscous Compressible Flow Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-17 Kai Koike
We construct a time-asymptotic expansion with pointwise remainder estimates for solutions to 1D compressible Navier–Stokes equations. The leading-order term is the well-known diffusion wave and the higher-order terms are a newly introduced family of waves which we call higher-order diffusion waves. In particular, these provide an accurate description of the power-law asymptotics of the solution around
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Gradient Higher Integrability for Degenerate Parabolic Double-Phase Systems Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-12 Wontae Kim, Juha Kinnunen, Kristian Moring
We prove a local higher integrability result for the gradient of a weak solution to degenerate parabolic double-phase systems of p-Laplace type. This result comes with reverse Hölder type estimates. The proof is based on a careful phase analysis, estimates in the intrinsic geometries and stopping time arguments.
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On Entropy Solutions of Scalar Conservation Laws with Discontinuous Flux Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-10 Evgeny Yu. Panov
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Weyl’s Law for the Steklov Problem on Surfaces with Rough Boundary Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-10 Mikhail Karpukhin, Jean Lagacé, Iosif Polterovich
The validity of Weyl’s law for the Steklov problem on domains with Lipschitz boundary is a well-known open question in spectral geometry. We answer this question in two dimensions and show that Weyl’s law holds for an even larger class of surfaces with rough boundaries. This class includes domains with interior cusps as well as “slow” exterior cusps. Moreover, the condition on the speed of exterior
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The Dean–Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-04 Federico Cornalba, Julian Fischer
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Regularity Properties of Passive Scalars with Rough Divergence-Free Drifts Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-03 Dallas Albritton, Hongjie Dong
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Highest Cusped Waves for the Burgers–Hilbert Equation Arch. Rational Mech. Anal. (IF 2.5) Pub Date : 2023-08-02 Joel Dahne, Javier Gómez-Serrano