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We consider the large time behavior of global strong solutions to the compressible viscoelastic flows on the whole space $\mathbb{R}^N\,(N\geq 2)$, where the system describes the elastic properties of the compressible fluid. Adding a…

Analysis of PDEs · Mathematics 2019-09-11 Qunyi Bie , Hui Fang , Qiru Wang , Zheng-an Yao

In this paper, we prove the existence of global weak solutions to the compressible two-fluid Navier-Stokes equations in three dimensional space. The pressure depends on two different variables from the continuity equations. We develop an…

Analysis of PDEs · Mathematics 2017-10-17 Alexis Vasseur , Huanyao Wen , Cheng Yu

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

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

We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains…

Analysis of PDEs · Mathematics 2015-07-21 John W. Barrett , Endre Süli

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

A compressible Oldroyd--B type model with stress diffusion is derived from a compressible Navier--Stokes--Fokker--Planck system arising in the kinetic theory of dilute polymeric fluids, where polymer chains immersed in a barotropic,…

Analysis of PDEs · Mathematics 2016-08-16 John W. Barrett , Yong Lu , Endre Süli

This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…

Analysis of PDEs · Mathematics 2026-05-29 Qinghao Lei , Weirong Liang

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N=2. We address the question of the global existence of strong solutions with large initial data for compressible Navier-Stokes system and Korteweg…

Analysis of PDEs · Mathematics 2012-11-21 Boris Haspot

This paper investigates the global dynamics of a three-dimensional fluid-particle interaction system that couples the compressible barotropic Navier-Stokes equations with the Vlasov-Fokker-Planck equation through a density-dependent…

Analysis of PDEs · Mathematics 2026-03-10 Fucai Li , Jinkai Ni , Dehua Wang

It is well known that the global well-posedness of the Navier-Stokes equations with temperature-dependent coefficients is a challenging problem, especially in multi-dimensional space. In this paper, we study the 3D Navier-Stokes equations…

Analysis of PDEs · Mathematics 2025-12-30 Yachun Li , Peng Lu , Zhaoyang Shang

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

This paper is dedicated to the global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows in the whole space $\mathbb{R}^n$ with any $n\geq2$. We aim at extending those works by Qian \& Zhang and…

Analysis of PDEs · Mathematics 2022-08-08 Xinghong Pan , Jiang Xu

In 1995, Kazhikhov and Vaigant introduced a particular class of isentropic compressible Navier-Stokes equations with variable viscosity coefficients and, for the first time, established the existence of global smooth solutions for…

Analysis of PDEs · Mathematics 2025-12-23 Jie Fan , Xiangdi Huang

In this paper, we are concerned with global existence and optimal decay rates of solutions for the three-dimensional compressible Hall-MHD equations. First, we prove the global existence of strong solutions by the standard energy method…

Analysis of PDEs · Mathematics 2015-05-05 Jincheng Gao , Zheng-an Yao

We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large.…

Analysis of PDEs · Mathematics 2025-10-28 Shuai Wang , Guochun Wu , Xin Zhong

For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…

Analysis of PDEs · Mathematics 2025-07-03 Qinghao Lei , Chengfeng Xiong

In this paper, we establish global strong solutions for arbitrarily large initial data to the 2D and 3D compressible Navier-Stokes-Korteweg system, also referred to as the quantum Navier-Stokes equations, originally derived by Dunn and…

Analysis of PDEs · Mathematics 2026-02-12 Xiangdi Huang , Yongteng Gu , Muxi Lei

We investigate a system describing the flow of a compressible two-component mixture. The system is composed of the compressible Navier-Stokes equations coupled with non-symmetric reaction-diffusion equations describing the evolution of…

Analysis of PDEs · Mathematics 2018-12-10 Tomasz Piasecki , Yoshihiro Shibata , Ewelina Zatorska

We study the initial-boundary value problem for 1D compressible MHD equations of viscous non-resistive fluids in the Lagrangian mass coordinates. Based on the estimates of upper and lower bounds of the density, weak solutions are…

Analysis of PDEs · Mathematics 2019-07-02 Yang Li , Yongzhong Sun