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In this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence…

Analysis of PDEs · Mathematics 2015-06-03 Haibo Cui , Huanyao Wen , Haiyan Yin

This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those…

Analysis of PDEs · Mathematics 2021-10-28 Suhua Lai , Hao Xu , Jianwen Zhang

This paper considers the Cauchy problem of equations for the viscous compressible and heat-conductive fluids in the two-dimensional(2D) space. We establish the local existence theory of unique strong solution under some initial layer…

Analysis of PDEs · Mathematics 2019-07-25 Zhilei Liang

The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…

Analysis of PDEs · Mathematics 2022-07-04 Jing Li , Boqiang Lü , Xue Wang

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

This paper concerns the Cauchy problem of the barotropic compressible Navier-Stokes equations on the whole two-dimensional space with vacuum as far field density. In particular, the initial density can have compact support. When the shear…

Analysis of PDEs · Mathematics 2013-06-21 Jing Li , Zhilei Liang

In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations with degenerate viscosities is considered. By introducing some new variables and making use of the "quasi-symmetric…

Analysis of PDEs · Mathematics 2019-04-09 Zhouping Xin , Shengguo Zhu

We give a necessary and sufficient condition for the global existence of the classical solution to the Cauchy problem of the compressible Euler-Poisson equations with radial symmetry. We introduce a new quantity which describes the balance…

Analysis of PDEs · Mathematics 2009-06-15 Satoshi Masaki

The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces.…

Analysis of PDEs · Mathematics 2010-10-22 Xianpeng Hu , Dehua Wang

In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations is considered. When viscosity coefficients are given as a constant multiple of the density's power ($\rho^\delta$ with…

Analysis of PDEs · Mathematics 2019-04-08 Zhouping Xin , Shengguo Zhu

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

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

We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that…

Analysis of PDEs · Mathematics 2024-08-20 Yachun Li , Peng Lu , Zhaoyang Shang

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

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

In this paper, we study the global well-posedness of classical solution to 2D Cauchy problem of the compressible Navier-Stokes equations with large initial data and vacuum. It is proved that if the shear viscosity $\mu$ is a positive…

Analysis of PDEs · Mathematics 2012-07-26 Quansen Jiu , Yi Wang , Zhouping Xin

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

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

The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in $\mathbb{R}^3$ remains a significant open problem. When there is no magnetic diffusion, even small data global well-posedness is…

Analysis of PDEs · Mathematics 2025-05-08 Jiahong Wu , Xiaoping Zhai

We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small.…

Analysis of PDEs · Mathematics 2022-11-16 Zilai Li , Hao Liu , Huaqiao Wang