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We consider the Cauchy problem for the isentropic compressible Euler-Maxwell equations under general pressure laws in a three-dimensional periodic domain. For any smooth initial electron density away from the vacuum and smooth…

Analysis of PDEs · Mathematics 2023-05-23 Shunkai Mao , Peng Qu

The full compressible magnetohydrodynamic system in three-dimensional exterior domains is investigated. For the initial-boundary-value problem of this system with slip boundary condition for the velocity, adiabatic one for the temperature,…

Analysis of PDEs · Mathematics 2022-11-02 Yunkun Chen , Yi Peng , Xue Wang

This paper is devoted to studying the Cauchy problem for the three-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosities given by $\mu=\rho^\alpha,\lambda=\rho^\alpha(\alpha>0)$. We establish the…

Analysis of PDEs · Mathematics 2025-07-23 Jie Fan , Xiangdi Huang , Anchun Ni

For smooth initial data, we establish the global existence and uniqueness of strong and classical solutions to the Cauchy problem for the barotropic compressible Navier-Stokes equations in two spatial dimensions with vacuum state as far…

Analysis of PDEs · Mathematics 2013-06-21 Xiangdi Huang , Jing Li

This paper concerns the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in the whole plane $\mathbb{R}^2$ with zero density at infinity. By spatial weighted energy method, we derive the local…

Analysis of PDEs · Mathematics 2022-05-18 Hong Chen , Xin Zhong

In this paper, we prove the global well-posedness of the classical solution to the 2D Cauchy problem of the compressible Navier-Stokes equations with arbitrarily large initial data when the shear viscosity $\mu$ is a positive constant and…

Analysis of PDEs · Mathematics 2012-09-04 Quansen Jiu , Yi Wang , Zhouping Xin

We consider the Cauchy problem for the full compressible Navier-Stokes equations with vanishing of density at infinity in R3. Our main purpose is to prove the existence (and uniqueness) of global strong and classical solutions and study the…

Analysis of PDEs · Mathematics 2017-02-22 Huanyao Wen , Changjiang Zhu

In this paper, we study the global well-posedness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum. With the assumption $\mu=const.$ and $\lambda=\rho^\beta,~\beta>1$ (Va\v{i}gant-Kazhikhov…

Analysis of PDEs · Mathematics 2014-09-22 Yu Mei

We investigate the Cauchy problem to the compressible planar non-resistive magnetohydrodynamic equations with zero heat conduction. The global existence of strong solutions to such a model has been established by Li and Li (J. Differential…

Analysis of PDEs · Mathematics 2023-02-17 Jinkai Li , Mingjie Li , Yang Liu , Xin Zhong

In this paper we study the initial-boundary-value problem for the barotropic compressible magnetohydrodynamic system with slip boundary conditions in three-dimensional exterior domain. We establish the global existence and uniqueness of…

Analysis of PDEs · Mathematics 2021-12-16 Yazhou Chen , Bin Huang , Xiaoding Shi

In this paper, we investigate the Cauchy problem of the compressible non-resistive MHD on $\mathbb{R}^2$ with vacuum as far field density. We prove that the 2D Cauchy problem has a unique local strong solution provided the initial density…

Analysis of PDEs · Mathematics 2018-01-03 Mingtao Chen , Aibin Zang

In this paper, we discuss the Cauchy Problem for the compressible isentropic Euler-Boltzmann equations with vacuum in radiation hydrodynamics. Firstly, we establish the local existence of regular solutions by the fundamental methods in the…

Mathematical Physics · Physics 2014-10-08 Yachun Li , Shengguo Zhu

We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density away from the vacuum, we construct infinitely many entropy…

Analysis of PDEs · Mathematics 2022-07-13 Vikram Giri , Hyunju Kwon

A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…

Differential Geometry · Mathematics 2020-01-08 Oliver Lindblad Petersen

This paper concerns the Cauchy problem of the nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact…

Analysis of PDEs · Mathematics 2015-06-17 Boqiang Lv , Zhonghai Xu , Xin Zhong

We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a…

Analysis of PDEs · Mathematics 2024-08-22 Yang Liu , Xin Zhong

We revisit the 2D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. For the initial density allowing vacuum at infinity, we derive the global existence and uniqueness of strong solutions…

Analysis of PDEs · Mathematics 2022-01-05 Xin Zhong

In this paper, we consider the Cauchy problem to the planar non-resistive magnetohydrodynamic equations without heat conductivity, and establish the global well-posedness of strong solutions with large initial data. The key ingredient of…

Analysis of PDEs · Mathematics 2021-06-01 Jinkai Li , Mingjie Li

This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy…

Analysis of PDEs · Mathematics 2018-01-24 Xin Zhong

We investigate global well-posedness to the Cauchy problem of three-dimensional compressible viscous and heat-conducting micropolar fluid equations with zero density at infinity. By delicate energy estimates, we establish global existence…

Analysis of PDEs · Mathematics 2022-03-15 Yang Liu , Xin Zhong