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In this paper, we study the global regularity and sharp decay rates for the isentropic hypo-viscous compressible Navier-Stokes equations in 1D. Firstly, we prove the global stability for the small initial data near a stable equilibrium.…

Analysis of PDEs · Mathematics 2026-03-17 Chen Liang , Zhaonan Luo , Zhaoyang Yin

We study global well-posedness of strong solutions for the nonhomogeneous Navier-Stokes equations with density-dependent viscosity and initial density allowing vanish in $\mathbb{R}^2$. Applying a logarithmic interpolation inequality and…

Analysis of PDEs · Mathematics 2021-03-01 Xin Zhong

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

We are concerned with compressible magneto-micropolar fluid equations (1.1)-(1.2). The global existence and large time behaviour of solutions near a constant state to the magneto-micropolar-Navier-Stokes-Poisson (MMNSP) system is…

Analysis of PDEs · Mathematics 2019-06-19 Cuiman Jia , Zhong Tan , Jianfeng Zhou

In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases.…

Analysis of PDEs · Mathematics 2025-03-20 Wenwen Huo , Chao Zhang

We investigate the global stability of large solutions to the compressible isentropic Navier-Stokes equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the strong solutions converge to…

Analysis of PDEs · Mathematics 2025-10-17 Yang Liu , Guochun Wu , Xin Zhong

We prove space-time decay estimates of suitable weak solutions to the Navier-Stokes Cauchy problem, corresponding to a given asymptotic behavior of the initial data of the same order of decay. We use two main tools. The first is a result…

Mathematical Physics · Physics 2016-03-23 Francesca Crispo , Paolo Maremonti

In this paper, we construct a class of global large solution to the compressible Navier-Stokes equations in the whole space $\R^d$. Precisely speaking, our choice of special initial data whose $\dot{B}^{-1}_{\infty,\infty}$ norm can be…

Analysis of PDEs · Mathematics 2019-03-26 Jinlu Li , Yanghai Yu , Weipeng Zhu , Zhaoyang Yin

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations without a solid core. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the…

Analysis of PDEs · Mathematics 2007-06-13 Ting Zhang , Daoyuan Fang

We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as…

Analysis of PDEs · Mathematics 2024-05-21 Xian Liao , Sagbo Marcel Zodji

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

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 investigate the optimal decay rate for the higher order spatial derivative of global solution to the compressible Navier-Stokes (CNS) equations with or without potential force in three-dimensional whole space. First of…

Analysis of PDEs · Mathematics 2021-08-06 Jincheng Gao , Minling Li , Zheng-an Yao

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

In this paper, we study the Navier-Stokes-Korteweg equations governed by the evolution of compressible fluids with capillarity effects. We first investigate the global well-posedness of solution in the critical Besov space for large initial…

Analysis of PDEs · Mathematics 2024-04-16 Zihao Song

Here we prove the existence of global in time regular solutions to the two-dimensional compressible Navier-Stokes equations supplemented with arbitrary large initial velocity $v\_0$ and almost constantdensity $\varrho\_0$, for large volume…

Analysis of PDEs · Mathematics 2016-03-24 Raphaël Danchin , Piotr B. Mucha

We consider the compressible Navier-Stokes-Korteweg system describing the dynamics of a liquid-vapor mixture with diffuse interphase. The global solutions are established under linear stability conditions in critical Besov spaces. In…

Analysis of PDEs · Mathematics 2019-05-22 Noboru Chikami , Takayuki Kobayashi

We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution.…

Analysis of PDEs · Mathematics 2024-01-04 Tsukasa Iwabuchi , Dáithí Ó hAodha

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 obtain the global large solutions to the compressible Navier-Stokes equations in $\mathbb{R}^2$. The solution is large in the sense that there is no smallness assumption applied to one component of the initial incompressible velocity.

Analysis of PDEs · Mathematics 2019-10-25 Xiaoping Zhai , Zhi-Min Chen