English
Related papers

Related papers: The asymptotic behavior of globally smooth solutio…

200 papers

In this paper we study the regularity of the non-cutoff Vlasov-Poisson-Boltzmann system for plasma particles of two species in the whole space $\mathbb{R}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions…

Analysis of PDEs · Mathematics 2021-09-22 Dingqun Deng

In this paper, the Cauchy problem for the multi-dimensional (M-D) bipolar Euler-Poisson equations with far field vacuum is considered. Based on physical observations and some elaborate analysis of this system's intrinsic symmetric…

Analysis of PDEs · Mathematics 2025-08-12 Zhongmin Qian , Liang Zhao , Shengguo Zhu

This paper investigates the asymptotic behavior of a hyperbolic relaxation system designed for homogeneous two-phase flows in the limit of vanishing relaxation time. The governing equations comprise conservation laws for mixture mass and…

Analysis of PDEs · Mathematics 2026-03-19 Huimin Yu

It is nowadays well understood that the multidimensional isentropic Euler system is desperately ill--posed. Even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail to ensure both…

Analysis of PDEs · Mathematics 2019-09-04 Dominic Breit , Eduard Feireisl , Martina Hofmanova

For one dimensional or multidimensional compressible Euler system of polytropic gases, it is well known that the smooth solution will generally develop singularities in finite time. However, for three dimensional Chaplygin gases, due to the…

Analysis of PDEs · Mathematics 2014-07-29 Ding Bingbing , Witt Ingo , Yin Huicheng

In this paper, we consider the compressible Euler-Maxwell equations arising in semiconductor physics, which take the form of Euler equations for the conservation laws of mass density and current density for electrons, coupled to Maxwell's…

Analysis of PDEs · Mathematics 2015-03-17 Jiang Xu

The system of compressible adiabatic flow through porous media is considered in $\mathbb{R}^{3}$ in the present paper. The global existence and uniqueness of classical solutions are obtained when the initial data is near its equilibrium. We…

Analysis of PDEs · Mathematics 2012-11-08 Guochun Wu Zhong Tan , Jun Huang

We investigate the relaxation problem and the diffusion phenomenon for the compressible Euler system with a time-dependent damping coefficient of the form $\tfrac{\mu}{(1+t)^{\lambda}}$ in $\mathbb{R}^d$ $(d \geq 1)$. We establish uniform…

Analysis of PDEs · Mathematics 2025-12-09 Timothée Crin-Barat , Xinghong Pan , Ling-Yun Shou , Qimeng Zhu

We study the three-dimensional isothermal Euler equations with linear damping and an exterior potential. For sufficiently large damping, we prove global well-posedness for arbitrarily large initial data by combining a parabolic comparison…

Analysis of PDEs · Mathematics 2025-09-30 Young-Pil Choi , Houzhi Tang , Weiyuan Zou

We compute the shear and bulk viscosities, as well as the thermal conductivity of an ultrarelativistic fluid obeying the relativistic Boltzmann equation in 2+1 space-time dimensions. The relativistic Boltzmann equation is taken in the…

Statistical Mechanics · Physics 2015-06-12 M. Mendoza , I. Karlin , S. Succi , H. J. Herrmann

The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. By using the dispersive Klein-Gordon effect, Guo \cite{Guo98} first…

Analysis of PDEs · Mathematics 2011-09-21 Juhi Jang , Dong Li , Xiaoyi Zhang

A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming the plasma is neutral and the electric field decays with sufficient rapidity as $t \to\infty$, we show that solutions can be constructed with arbitrarily…

Analysis of PDEs · Mathematics 2025-02-06 Grace Mattingly , Stephen Pankavich , Jonathan Ben-Artzi

We investigate the large-time behavior of the pressureless Euler system with nonlocal velocity alignment and interaction forces, with the aim of characterizing the asymptotic convergence of classical solutions under general interaction…

Analysis of PDEs · Mathematics 2025-10-29 José A. Carrillo , Young-Pil Choi , Dowan Koo , Oliver Tse

In this work, we investigate the difference estimate for a class of Euler-Maxwell system and those of magnetohydrodynamics (in short, MHD) systems in three dimensions. We decompose the Euler-Maxwell system into three parts, namely the MHD…

Analysis of PDEs · Mathematics 2025-04-29 Dong-ha Kim , Junha Kim , Jihoon Lee

We consider a linearized Euler--Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. We present the derivation of the model, and we show its well-posedeness, its strong and polynomial stability…

Analysis of PDEs · Mathematics 2021-05-28 Simon Labrunie , Ibtissem Zaafrani

We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric initial data with compact support. In particular, we prove that…

Analysis of PDEs · Mathematics 2022-09-20 Jonathan Ben-Artzi , Baptiste Morisse , Stephen Pankavich

In this paper we discuss the dissipative property of near-equilibrium classical solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann System in the whole space $\R^3$ when the positive charged ion flow provides a spatially uniform…

Analysis of PDEs · Mathematics 2011-07-12 Renjun Duan

In this paper, we investigate a three-dimensional fluid-particle coupled model. % in whole space $\mathbb{R}^3$. This model combines the full compressible Navier-Stokes equations with the Vlasov-Fokker-Planck equation via the momentum and…

Analysis of PDEs · Mathematics 2024-08-27 Fucai Li , Jinkai Ni , Man Wu

We study a one-dimensional system of cold plasma equations taking into account electron-ion collisions in both relativistic and nonrelativistic cases. It is known that for a constant collision coefficient $\nu$, the solution to the Cauchy…

Computational Physics · Physics 2026-02-05 Evgeniy V. Chizhonkov , Olga S. Rozanova

In this paper, we consider the asymptotic behavior of global solutions to 3D anisotropic incompressible MHD systems. For the 3D MHD system with horizontal dissipation and full magnetic diffusion, it is shown that $\uh(t)$ decays at the rate…

Analysis of PDEs · Mathematics 2022-07-15 Yang Li