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In the realm of mathematical fluid dynamics, a formidable challenge lies in establishing inviscid limits from the Navier-Stokes equations to the Euler equations, wherein physically admissible solutions can be discerned. The pursuit of…

Analysis of PDEs · Mathematics 2025-09-11 Geng Chen , Moon-Jin Kang , Alexis F. Vasseur

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 study the high Reynolds number limit of a viscous fluid in the presence of a rough boundary. We consider the two-dimensional incompressible Navier-Stokes equations with Navier slip boundary condition, in a domain whose boundaries exhibit…

Analysis of PDEs · Mathematics 2017-06-23 David Gérard-Varet , Christophe Lacave , Toan T. Nguyen , Frédéric Rousset

We consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a bounded domain driven by time periodic inflow/outflow boundary conditions. We show that the problem admits a time periodic…

Analysis of PDEs · Mathematics 2021-01-20 Anna Abbatiello , Eduard Feireisl

We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier-Stokes system on a thin domain. In particular, the existence of solutions to the Navier-Stokes system with…

Analysis of PDEs · Mathematics 2017-05-22 I. S. Ciuperca , E. Feireisl , M. Jai , A. Petrov

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 are concerned with the linear stability of the Couette flow for the non-isentropic compressible Navier-Stokes equations with vanished shear viscosity in a domain $\mathbb{T}\times \mathbb{R}$. For a general initial data settled in…

Analysis of PDEs · Mathematics 2021-07-08 Xiaoping Zhai

This paper studies the two-dimensional inhomogeneous Navier--Stokes equations governing stratified flows in a bounded domain under a gravitational potential \(f\). Our main results are as follows. First, we provide a rigorous…

Analysis of PDEs · Mathematics 2025-12-23 Song Jiang , Quan Wang

We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…

Analysis of PDEs · Mathematics 2025-11-07 Josef Demmel , Emil Wiedemann

We show the existence of (a class of) weak solutions to the three-dimensional stationary incompressible inhomogeneous Navier--Stokes equations with density-dependent viscosity coefficient in the axially symmetric case. Further symmetric…

Analysis of PDEs · Mathematics 2025-01-08 Zihui He

This paper investigates the local existence and uniqueness of strong solutions to the three-dimensional compressible Navier-Stokes equations with density-dependent viscosities in exterior domains. When both the shear and bulk viscosity…

Analysis of PDEs · Mathematics 2025-12-09 Hairong Liu , Hua Zhong

We investigate the initial-value problem for the incompressible tangential Navier-Stokes equation with variable viscosity on a given two-dimensional surface without boundary. Existence of global weak and strong solutions under inhomogeneous…

Analysis of PDEs · Mathematics 2024-12-10 Andrea Poiatti , Ulisse Stefanelli

In the present paper, it is shown that the large amplitude viscous shock wave is nonlinearly stable for isentropic Navier-Stokes equations, in which the pressure could be general and includes $\gamma$-law, and the viscosity coefficient is a…

Analysis of PDEs · Mathematics 2019-10-22 Lin He , Feimin Huang

This paper studies the incompressible limit of global strong solutions to the three-dimensional compressible Navier-Stokes equations associated with Navier's slip boundary condition, provided that the time derivatives, up to first order, of…

Analysis of PDEs · Mathematics 2013-09-03 Yaobin Ou , Dandan Ren

Here we prove the all-time propagation of the Sobolev regularity for the velocity field solution of the two-dimensional compressible Navier-Stokes equations, provided the volume (bulk) viscosity coefficient is large enough. The initial…

Analysis of PDEs · Mathematics 2021-03-03 Raphaël Danchin , Piotr Boguslaw Mucha

In this paper, we investigate the well-posedness theory and exponential stability for the inhomogeneous incompressible Navier-Stokes equation with only horizontal dissipative structure. Due to the lack of the vertical dissipative term and…

Analysis of PDEs · Mathematics 2023-11-28 Jincheng Gao , Lianyun Peng , Zheng-an Yao

In this paper, the one-dimensional compressible Navier-Stokes system with outer pressure boundary conditions is investigated. Under some suitable assumptions, we prove that the specific volume and the temperature are bounded from below and…

Analysis of PDEs · Mathematics 2022-06-01 Guocai Cai , Canpei Chen , Yanfang Peng

We are concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system with degenerate heat-conductivity describing the one-dimensional…

Analysis of PDEs · Mathematics 2024-07-19 Kexin Li , Xiaojing Xu

We study the large-time behavior of solutions to the compressible Navier-Stokes equations for a viscous and heat-conductive gases in $\mathbb{R}^3$. More precisely, under a suitable additional condition involving only the low frequencies of…

Analysis of PDEs · Mathematics 2020-07-15 Xiaoping Zhai , Zhi-Min Chen

This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity…

Analysis of PDEs · Mathematics 2016-12-26 Xin Liu