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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

Motivated by \cite{CG10,CZ6}, we prove the global existence of solutions to the two-dimensional isentropic compressible Navier-Stokes equations with smooth initial data which are slowly varying in one direction and with initial density…

Analysis of PDEs · Mathematics 2021-06-04 Yong Lu , Ping Zhang

This paper studies the global well-posedness of classical solutions to the isentropic compressible Navier-Stokes equations in 3D domains D under non-slip boundary conditions. D will separate into the inner and boundary parts along a free…

Analysis of PDEs · Mathematics 2024-10-15 Xinyu Fan , Jing Li

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

In this paper, we consider the Cauchy problem to the heat conductive compressible Navier-Stokes equations in the presence of vacuum and with vacuum far field. Global well-posedness of strong solutions is established under the assumption,…

Analysis of PDEs · Mathematics 2020-05-20 Jinkai Li

We are concerned with the long-time behavior of classical solutions to the isentropic compressible Navier-Stokes equations in $\mathbb R^3$. Our main results and innovations can be stated as follows: Under the assumption that the density…

Analysis of PDEs · Mathematics 2024-11-05 Guochun Wu , Xin Zhong

The purpose of this work is to investigate the Cauchy problem of global-in-time existence of large strong solutions to the Navier-Stokes equations for compressible viscous and heat conducting fluids. A class of density-dependent viscosity…

Analysis of PDEs · Mathematics 2024-12-04 Yachun Li , Peng Lu , Zhaoyang Shang , Shaojun Yu

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

We consider the global existence and large-time asymptotic behavior of strong solutions to the Cauchy problem of the three-dimensional nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity and vacuum. We…

Analysis of PDEs · Mathematics 2021-01-12 Cheng He , Jing Li , Boqiang Lü

We establish the global-in-time existence of solutions of the Cauchy problem for the full Navier-Stokes equations for compressible heat-conducting flow in multidimensions with initial data that are large, discontinuous, spherically…

Analysis of PDEs · Mathematics 2022-08-11 Gui-Qiang G. Chen , Yucong Huang , Shengguo Zhu

We consider the Cauchy problem of the non-isentropic compressible magnetohydrodynamic equations in $\mathbb{R}^3$ with far-field vacuum. By deriving delicate energy estimates and exploiting the intrinsic structure of the system, we…

Analysis of PDEs · Mathematics 2025-12-24 Lin Xu , Xin Zhong

We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density. The central feature of the solutions is the…

Analysis of PDEs · Mathematics 2022-02-17 Gui-Qiang G. Chen , Yong Wang

We investigate the barotropic compressible Navier-Stokes equations with slip boundary conditions in a three-dimensional (3D) simply connected bounded domain, whose smooth boundary has a finite number of two-dimensional connected components.…

Analysis of PDEs · Mathematics 2025-04-23 Guocai Cai , Jing Li

In this paper, we prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation. The main contribution of this paper…

Analysis of PDEs · Mathematics 2016-12-21 Alexis F. Vasseur , Cheng Yu

We prove the global-in-time existence of weak solutions to the Navier-Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent $\gamma\ge1$. Initial data and solutions are small in $L^2$ around a…

Analysis of PDEs · Mathematics 2015-05-30 Anthony Suen

We consider the initial-boundary-value problem of the isentropic compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile in 3D bounded domain with slip boundary condition and vacuum. The global…

Analysis of PDEs · Mathematics 2021-03-08 Yazhou Chen , Bin Huang , Xiaoding Shi

We consider the isentropic compressible Navier-Stokes-Poisson equations with degenerate viscousities and vacuum in a three-dimensional torus. The local well-posedness of classical solution is established by introducing a "quasi-symmetric…

Analysis of PDEs · Mathematics 2024-07-24 Peng Lu , Shaojun Yu

We consider the 3D isentropic compressible Navier-Stokes equations with degenerate viscousities and vacuum. The degenerate viscosities $\mu(\rho)$ and $\lambda(\rho)$ are proportional to some power of density, while the powers of density in…

Analysis of PDEs · Mathematics 2024-09-30 Yachun Li , Shaojun Yu

We revisit the 3D Cauchy problem of compressible heat-conducting magnetohydrodynamic equations with vacuum as far field density. By delicate energy method, we derive global existence and uniqueness of strong solutions provided that…

Analysis of PDEs · Mathematics 2022-08-01 Yang Liu , Xin Zhong

This paper concerns the isentropic compressible Navier-Stokes equations in a three-dimensional (3D) bounded domain with slip boundary conditions and vacuum. It is shown that the classical solutions to the initial-boundary-value problem of…

Analysis of PDEs · Mathematics 2025-01-14 Saiguo Xu , Yinghui Zhang