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Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…

Analysis of PDEs · Mathematics 2025-02-12 Shengxin Li , Tong Yang , Zhu Zhang

We construct a time-asymptotic expansion with pointwise remainder estimates for solutions to 1D compressible Navier--Stokes equations. The leading-order term is the well-known diffusion wave and the higher-order terms are newly introduced…

Analysis of PDEs · Mathematics 2023-09-12 Kai Koike

We investigate the high viscosity limit (also called inertial limit) of the barotropic compressible Navier-Stokes equations supplemented with initial data which are perturbations of a stable constant solution. In the case of constant…

Analysis of PDEs · Mathematics 2026-03-17 Raphaël Danchin

We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…

Analysis of PDEs · Mathematics 2020-09-24 Ling Wan , Tao Wang

In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of…

Analysis of PDEs · Mathematics 2025-12-01 Nilasis Chaudhuri , Francesco Fanelli , Yang Li , Ewelina Zatorska

We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-Stokes-Fourier system. Our main result is the existence of a weak solution to these…

Analysis of PDEs · Mathematics 2007-09-24 Piotr B. Mucha , Milan Pokorny

We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of…

Fluid Dynamics · Physics 2016-12-16 Davide Modesti , Sergio Pirozzoli

We prove the existence and uniqueness of strong solutions to the steady isentropic compressible Navier-Stokes equations with inflow boundary conditions for density and mixed boundary conditions for the velocity around a shear flow. In…

Analysis of PDEs · Mathematics 2022-04-19 Wen-Gang Yang

In this paper we consider the one-dimensional Navier-Stokes system for a heat-conducting, compressible reacting mixture which describes the dynamic combustion of fluids of mixed kinds on unbounded domains. This model has been discussed on…

Analysis of PDEs · Mathematics 2026-02-24 Siran Li

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter $\ep \to 0$ and the fluid is confined to an exterior spatial domain $\Omega_\ep$ that may vary with…

Analysis of PDEs · Mathematics 2015-04-01 Eduard Feireisl , Trygve K. Karper , Ondrej Kreml , Jan Stebel

This paper aims at justifying the low Mach number convergence to the incompressible Navier-Stokes equations for viscous compressible flows in the ill-prepared data case. The fluid domain is either the whole space, or the torus. A number of…

Analysis of PDEs · Mathematics 2014-09-26 Raphaël Danchin , Lingbing He

In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is…

Analysis of PDEs · Mathematics 2010-04-02 Quansen Jiu , Yi Wang , Zhouping Xin

In this paper, we consider a singular limit problem for a diffuse interface model for two immiscible compressible viscous fluids. Via a relative entropy method, we obtain a convergence result for the low Mach number limit to a corresponding…

Analysis of PDEs · Mathematics 2024-11-15 Helmut Abels , Yadong Liu , Šárka Nečasová

In this paper, we study the asymptotic behavior of solutions to the compressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length…

This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, Matsumura and Nishihara showed in [A. Matsumura and K. Nishihara, Large-time behaviors of solutions to an…

Analysis of PDEs · Mathematics 2020-09-24 Lili Fan , Hongxia Liu , Tao Wang , Huijiang Zhao

Regularity and uniqueness of weak solution of the compressible isentropic Navier-Stokes equations is proven for small time in dimension $N=2,3$ under periodic boundary conditions. In this paper, the initial density is not required to have a…

Analysis of PDEs · Mathematics 2010-01-12 Boris Haspot

The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for…

Analysis of PDEs · Mathematics 2008-11-26 Hai-Liang Li , Jing Li , Zhouping Xin

We establish the incompressible Navier--Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian.…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 A. Bellouquid

We consider the one-dimensional compressible Navier--Stokes system for a viscous and heat-conducting ideal polytropic gas when the viscosity $\mu$ and the heat conductivity $\kappa$ depend on the specific volume $v$ and the temperature…

Analysis of PDEs · Mathematics 2020-09-24 Tao Wang , Huijiang Zhao

We give an existence and asymptotic result for the so-called finite energy weak martingale solution of the compressible isentropic Navier--Stokes system driven by some random force in the whole spatial region. In particular, given a general…

Analysis of PDEs · Mathematics 2017-05-04 Prince Romeo Mensah