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We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in three spatial dimensions with smooth initial data which are of small energy but…

Mathematical Physics · Physics 2015-03-17 Xiangdi Huang , Jing Li , Zhouping Xin

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 is concerned with the global existence and uniqueness of classical solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in three-dimensional bounded domains or in the whole space…

Analysis of PDEs · Mathematics 2026-05-01 Qinghao Lei

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

A fluid-particle model is investigated in the present paper, which consists of the compressible Navier-Stokes equations coupled with the Vlasov equation though a nonlinear drag force. We consider the initial value problem for the…

Analysis of PDEs · Mathematics 2021-09-17 Hai-Liang Li , Ling-Yun Shou

A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2017-04-06 Fucai Li , Yanmin Mu , Dehua Wang

This paper is concerned with a diffuse interface model for the gas-liquid phase transition. The model consists the compressible Navier-Stokes equations with van der Waals equation of state and a modified Allen-Cahn equation. The global…

Analysis of PDEs · Mathematics 2018-10-02 Qiaolin He , Ming Mei , Xiaoding Shi , Xiaoping Wang

In this paper, we consider the three-dimensional isentropic Navier-Stokes equations for compressible fluids with viscosities depending on density in a power law and allowing initial vacuum. We introduce the notion of regular solutions and…

Analysis of PDEs · Mathematics 2015-04-14 Yachun Li , Ronghua Pan , Shengguo Zhu

This paper is dedicated to the study of the inviscid liquid-gas two-phase flow model in $\mathbb{R}^d\ (d\geq1)$. We establish the global existence of strong solutions to this system with small initial data in hybrid Besov spaces based on…

Analysis of PDEs · Mathematics 2024-04-09 Zhigang Wu , Mengqian Liu , Juanzi Cai

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

In this paper, we study the Cauchy problem of a two-phase flow system consisting of the compressible isothermal Euler equations and the incompressible Navier-Stokes equations coupled through the drag force, which can be formally derived…

Analysis of PDEs · Mathematics 2024-02-01 Feimin Huang , Houzhi Tang , Guochun Wu , Weiyuan Zou

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

In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier-Stokes equations where the coupling of two equations is through the drag force. We…

Analysis of PDEs · Mathematics 2021-10-04 Young-Pil Choi , Jinwook Jung

In this work, we study the global existence of strong solutions and large-time behavior of a two-phase fluid model in a bounded domain. The model consists of the isothermal Euler equations and the isentropic compressible Navier--Stokes…

Analysis of PDEs · Mathematics 2021-01-01 Jinwook Jung

In this paper, we consider the Cauchy problem of the multi-dimensional compressible Navier-Stokes-Euler system for two-phase flow motion, which consists of the isentropic compressible Navier-Stokes equations and the isothermal compressible…

Analysis of PDEs · Mathematics 2024-08-09 Hai-Liang Li , Ling-Yun Shou

In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable…

Analysis of PDEs · Mathematics 2024-08-09 Xiangdi Huang , Jiaxu Li , Rong Zhang

In this paper, we are concerned with the global existence and optimal rates of strong solutions for three-dimensional compressible viscoelastic flows. We prove the global existence of the strong solutions by the standard energy method under…

Analysis of PDEs · Mathematics 2012-09-26 Xianpeng Hu , Guochun Wu

In this paper we are concerned with the global existence of smooth solutions to the turbulent flow equations for compressible flows in $\mathbb{R}^3$. The global well-posedness is proved under the condition that the initial data are close…

Analysis of PDEs · Mathematics 2012-04-10 Dongfen Bian , Boling Guo

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

In this paper, we investigate the existence of a global classical solution to 3D Cauchy problem of the isentropic compressible Navier-Stokes equations with large initial data and vacuum. Precisely, when the far-field density is vacuum…

Analysis of PDEs · Mathematics 2015-07-07 Xiaofeng Hou , Hongyun Peng , Changjiang Zhu