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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

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

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space $\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D nonhomogeneous…

Analysis of PDEs · Mathematics 2017-10-20 Lin Li , Qiao Liu , Xin Zhong

We study the three-dimensional Cauchy problem for a non-isothermal compressible nematic liquid crystal system with far-field vacuum. By deriving refined energy estimates and exploiting the coupled structure of the equations, we establish…

Analysis of PDEs · Mathematics 2025-12-30 Lin Xu , Xin Zhong

We consider a generalization of the compressible barotropic Navier-Stokes equations to the case of non-Newtonian fluid in the whole space. The viscosity tensor is assumed to be coercive with an exponent $q>1.$ We prove that if the total…

Analysis of PDEs · Mathematics 2010-09-28 Olga Rozanova

This paper is concerned with the Cauchy problem for the modified two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity. By fully using the structure of the system, we can obtain the key…

Analysis of PDEs · Mathematics 2026-02-02 Bing Yuan , Rong Zhang , Peng Zhou

We investigate the Cauchy problem of three-dimensional compressible non-isothermal nematic liquid crystal flows in $\mathbb{R}^3$. We derive the global existence and uniqueness of strong solutions with both interior and far field vacuum…

Analysis of PDEs · Mathematics 2021-08-24 Yang Liu , Xin Zhong

We study the Cauchy problem of three-dimensional compressible non-isentropic magnetohydrodynamic (MHD) fluids with both interior and far field vacuum states. Applying delicate energy estimates, initial layer analysis, and continuation…

Analysis of PDEs · Mathematics 2024-08-23 Yang Liu , Xin Zhong

This paper studies the Cauchy problem for three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic equations with vacuum as far field density. We prove the global existence and uniqueness of strong solutions provided…

Analysis of PDEs · Mathematics 2021-05-04 Yang Liu , Xin Zhong

This paper considers the two-dimensional Cauchy problem of the full compressible Navier-Stokes equations with far-field vacuum in $\mathbb{R}^2$, where the viscosity and heat-conductivity coefficients depend on the absolute temperature…

Analysis of PDEs · Mathematics 2025-04-15 Yue Cao , Xun Jiang

The authors study the Cauchy problem of the magnetohydrodynamic equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For two spatial dimensions, we establish the global…

Analysis of PDEs · Mathematics 2014-05-21 Boqiang Lv , Xiaoding Shi , Xinying Xu

We study the singularity formation of strong solutions to the two-dimensional (2D) Cauchy problem of the non-baratropic compressible magnetohydrodynamic equations without heat conductivity. It is proved that the strong solution exists…

Analysis of PDEs · Mathematics 2018-09-05 Xin Zhong

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…

Analysis of PDEs · Mathematics 2018-04-30 Boqiang Lv , Xiaoding Shi , Xin Zhong

We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no-slip boundary conditions for the velocity. No external body…

Analysis of PDEs · Mathematics 2026-01-26 Anna Abbatiello , Miroslav Bulíček , Petr Kaplický

We consider the Cauchy problem for one-dimensional (1D) barotropic compressible Navier-Stokes equations with density-dependent viscosity and large external force. Under a general assumption on the density-dependent viscosity, we prove that…

Analysis of PDEs · Mathematics 2018-08-24 Kexin Li , Boqiang Lü , Yixuan Wang

This paper studies the local existence of strong solutions to the Cauchy problem of the 2D fluid-particle interaction model with vacuum as far field density. Notice that the technique used by Ding et al.\cite{SBH} for the corresponding 3D…

Analysis of PDEs · Mathematics 2016-09-04 Yang Liu

In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fields. Global well-posedness of strong solutions is established…

Analysis of PDEs · Mathematics 2021-12-20 Jinkai Li , Qiang Tao

The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the…

Analysis of PDEs · Mathematics 2020-10-20 Fuyi Xu , Meiling Chi , Lishan Liu , Yonghong Wu

The entropy is one of the fundamental states of a fluid and, in the viscous case, the equation that it satisfies is highly singular in the region close to the vacuum. In spite of its importance in the gas dynamics, the mathematical analyses…

Analysis of PDEs · Mathematics 2017-10-19 Jinkai Li , Zhouping Xin

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
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