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Global well-posedness and inviscid limit of the compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent friction force

This paper establishes the global well-posedness, uniform-in-viscosity estimates, and optimal large-time decay rates for classical solutions to the three-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent friction, thereby rigorously justifying the global inviscid limit and proving the first global existence of classical solutions for the corresponding Euler-Vlasov-Fokker-Planck system.

Fucai Li, Jinkai Ni, Dehua WangTue, 10 Ma🔢 math

Wellposedness and asymptotic behavior of solutions for the quintic wave equation with nonlocal dissipation

This paper establishes the wellposedness and polynomial energy decay of solutions for a quintic defocusing wave equation with nonlinear, energy-dependent damping by combining Galerkin approximations, Strichartz estimates, and an adapted Nakao method to overcome critical nonlinearity challenges.

Marcelo Cavalcanti, Valéria Domingos Cavalcanti, Josiane Faria, Cintya OkawaTue, 10 Ma🔢 math

Global Weak Solutions of a Navier-Stokes-Cahn-Hilliard System for Incompressible Two-phase flows with Thermo-induced Marangoni Effects

This paper establishes the existence of global weak solutions for a Navier-Stokes-Cahn-Hilliard system modeling thermo-induced Marangoni effects in two-phase incompressible flows with variable physical parameters and singular potentials in both two and three dimensions, while also proving solution uniqueness in the two-dimensional case under matched density conditions.

Lingxi Chen, Hao WuTue, 10 Ma🔢 math

Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions

This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations modeling Micro-Electro-Mechanical Systems (MEMS) under Dirichlet boundary conditions, establishing their convergence to equilibrium with rate estimates and supporting numerical simulations.

Wenlong Wu, Yanyan ZhangTue, 10 Ma🔢 math

Well-posedness and asymptotic behavior of solutions to a second order nonlocal parabolic MEMS equation

This paper establishes the local and global well-posedness, quenching criteria, and asymptotic convergence rates (exponential or algebraic) of solutions to a second-order nonlocal parabolic MEMS equation by employing operator semigroups, Lojasiewicz–Simon inequalities, and numerical validation.

Yufei Wei, Yanyan ZhangTue, 10 Ma🔢 math

Sharp quantitative integral inequalities for general conformally invariant extensions

This paper establishes sharp quantitative integral inequalities for a general family of conformally invariant extension operators and their adjoints by developing a refined analysis of hypergeometric functions, thereby extending previous results to the full admissible parameter range.

Qiaohua Yang, Shihong ZhangTue, 10 Ma🔢 math

On the global dynamics and blow-up dichotomy for inhomogeneous coupled nonlinear Schrödinger systems

This paper establishes a sharp criterion for the global existence versus finite-time blow-up dichotomy of solutions to an inhomogeneous coupled nonlinear Schrödinger system with quadratic interactions by utilizing variational methods, conservation laws, and sharp Gagliardo-Nirenberg inequalities relative to ground state solutions.

Mykael Cardoso, Lázaro GilTue, 10 Ma🔢 math

Rate-Induced Tipping in a Non-Uniformly Moving Habitat and Determination of the Critical Rate

This paper investigates rate-induced tipping in a moving habitat using a non-autonomous reaction-diffusion model, demonstrating that populations face extinction if the habitat's displacement rate exceeds a unique critical threshold, a phenomenon analytically characterized by heteroclinic connections between stable and unstable states.

Blake Barker, Emmanuel Fleurantin, Matt Holzer, Christopher K. R. T. Jones, Sebastian WieczorekTue, 10 Ma🔢 math

Forcing Effects on Finite-Time Blow-Up in Degenerate and Singular Parabolic Equations

This paper establishes critical exponents that determine whether solutions to a degenerate and singular parabolic equation with a time-dependent forcing term exhibit finite-time blow-up or global existence, proving that blow-up is inevitable for positive forcing exponents while identifying specific thresholds for global solvability under smallness conditions when the forcing is constant or subcritical.

Mohamed Majdoub, Berikbol T. TorebekTue, 10 Ma🔢 math

An asymptotic model of Poisson--Nernst--Planck--Stokes systems in narrow channels

This paper presents a systematic asymptotic reduction of the Poisson–Nernst–Planck–Stokes equations for narrow channels that remains valid even when the Debye length is comparable to the channel width, enabling the prediction of complex ion transport phenomena such as counter-gradient ion flow and enhanced selectivity due to finite-size effects.

Christine Keller, Andreas Münch, Barbara WagnerTue, 10 Ma🔬 physics

Chemotaxis with tomography

This paper investigates how topographical obstacles influence cell chemotaxis by modifying the Keller-Segel model with a spatially dependent chemotaxis coefficient, demonstrating that this modification is crucial for preventing cell concentration blow-up.

Valeria Cuentas, Elio EspejoTue, 10 Ma🔬 physics

A global well-posedness result for the three-dimensional inviscid quasi-geostrophic equation over a cylindrical domain

This paper establishes the global existence and uniqueness of generalized solutions for the three-dimensional inviscid quasi-geostrophic equation on a cylindrical domain with a multiply connected cross-section under specific Neumann and no-flux boundary conditions, assuming the initial potential vorticity is essentially bounded.

Qingshan ChenTue, 10 Ma🔬 physics

Weak Singularity of Navier-Stokes Equations Based on Energy Estimation in Sobolev Space

This paper argues that for steady, fully developed incompressible Navier-Stokes flows, the condition where the total mechanical energy gradient is perpendicular to the streamline causes the viscous term to vanish and the solution to lose $H^1$ -regularity, thereby creating a weak singularity where the equations degenerate into the Euler equations.

Chio Chon KitTue, 10 Ma🔬 physics

Learning embeddings of non-linear PDEs: the Burgers' equation

This paper proposes a Physics Informed Neural Network framework with multi-head linear layers and orthogonality constraints to construct robust, interpretable low-dimensional embeddings for the viscous Burgers' equation, demonstrating that a small number of latent modes effectively capture the solution space's dominant dynamics.

Pedro Tarancón-Álvarez, Leonid Sarieddine, Pavlos Protopapas, Raul JimenezTue, 10 Ma🤖 cs.LG

Partial Differential Equations in the Age of Machine Learning: A Critical Synthesis of Classical, Machine Learning, and Hybrid Methods

This critical review synthesizes classical and machine learning approaches for solving partial differential equations by contrasting their deductive and inductive epistemologies, identifying three genuine complementarities, and establishing principles for hybrid methods that rigorously address error budgets and structural guarantees across emerging computational frontiers.

Mohammad Nooraiepour, Jakub Wiktor Both, Teeratorn Kadeethum, Saeid SadeghnejadTue, 10 Ma🤖 cs.LG

Quantitative evaluations of stability and convergence for solutions of semilinear Klein--Gordon equation

This paper proposes quantitative evaluation methods for assessing the stability and convergence of numerical solutions to the semilinear Klein–Gordon equation with power-law nonlinearity, while investigating optimal thresholds based on variations in initial value amplitude and mass.

Takuya Tsuchiya, Makoto NakamuraTue, 10 Ma⚛️ quant-ph

Green--Wasserstein Inequality on Compact Surfaces

This paper resolves a question posed by Steinerberger by proving that the $\sqrt{\log n}$ factor in the two-dimensional Green–Wasserstein inequality is necessary and cannot be removed while maintaining a uniform $O(n^{-1/2})$ remainder for point sets on compact connected surfaces.

Maja GwozdzThu, 12 Ma🔢 math

Quasi-linear equation $\Delta_pv+av^q=0$ on manifolds with integral bounded Ricci curvature and geometric applications

This paper establishes Liouville theorems, nonexistence results, and gradient estimates for solutions to the quasi-linear equation $\Delta_p v + a v^q = 0$ on complete Riemannian manifolds satisfying a $\chi$ -type Sobolev inequality with integral-bounded negative Ricci curvature, leading to new geometric applications such as proving that manifolds with non-negative Ricci curvature outside a compact set and sufficiently small $L^{n/2}$ -norm of negative Ricci curvature possess exactly one end.

Youde Wang, Guodong Wei, Liqin ZhangThu, 12 Ma🔢 math

Existence of All Wilton Ripples of the Kawahara Equation

This paper establishes the existence of Wilton ripple solutions for the Kawahara equation for all integer values of $K \geq 2$ by employing a Lyapunov-Schmidt reduction, thereby extending previous results that were limited to the specific case of $K=2$ .

Ryan P. CreedonThu, 12 Ma🔢 math

Some properties of the principal Dirichlet eigenfunction in Lipschitz domains, via probabilistic couplings

This paper establishes uniform regularity estimates for the principal Dirichlet eigenfunctions of both discrete random walks and continuous Brownian motion in Lipschitz domains by employing a novel probabilistic approach combining Feynman-Kac representations, gambler's ruin estimates, and a new "multi-mirror" coupling, while also reviewing convergence results between the discrete and continuous eigenfunctions.

Quentin Berger, Nicolas BouchotThu, 12 Ma🔢 math

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