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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 convergence rate of a finite volume approximation of the compressible Navier--Stokes--Fourier system. To this end we first show the local existence of a highly regular unique strong solution and analyse its global…

Numerical Analysis · Mathematics 2022-10-28 Danica Basaric , Maria Lukacova-Medvidova , Hana Mizerova , Bangwei She , Yuhuan Yuan

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

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations…

Analysis of PDEs · Mathematics 2015-08-26 Alexis F. Vasseur , Cheng Yu

In this paper we give a new formulation of the compressible Navier-Stokes by introducing an suitable effective velocity $v=u+\n\va(\rho)$ provided that the viscosity coefficients verify the algebraic relation of \cite{BD}. We give in…

Analysis of PDEs · Mathematics 2014-11-21 Boris Haspot

In this work we consider the Navier-Stokes problem modified by the absorption term $|\textbf{u}|^{\sigma-2}\textbf{u}$, where $\sigma>1$, which is introduced in the momentum equation. % For this new problem, we prove the existence of weak…

Analysis of PDEs · Mathematics 2009-04-01 Hermenegildo Borges de Oliveira

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 prove global existence of weak solutions for the stationary compressible Navier-Stokes equations with an anisotropic and nonlocal viscous term in a periodic domain. This gives an answer to an open problem important for…

Analysis of PDEs · Mathematics 2020-04-10 D. Bresch , Cosmin Burtea

So far existence of dissipative weak solutions for the compressible Navier-Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e.,…

Analysis of PDEs · Mathematics 2019-05-08 Young-Sam Kwon , Antonin Novotny , Vladyslav Satko

The steady compressible Navier--Stokes--Fourier system is considered, with either Dirichlet or Navier boundary conditions for the velocity and the heat flux on the boundary proportional to the difference of the temperature inside and…

Analysis of PDEs · Mathematics 2015-11-23 Piotr B. Mucha , Milan Pokorný , Ewelina Zatorska

We introduce the new concept of maximal dissipative solutions for a general class of isothermal GENERIC systems. Under certain assumption, we show that maximal dissipative solutions are well posed as long as the bigger class of dissipative…

Analysis of PDEs · Mathematics 2023-12-22 Robert Lasarzik

In this paper we prove the existence of global weak dissipative martingale solutions for a one-dimensional compressible fluid model with capillarity and density dependent viscosity, driven by random initial data and a stochastic forcing…

Analysis of PDEs · Mathematics 2024-12-17 Donatella Donatelli , Lorenzo Pescatore , Stefano Spirito

We establish the global well-posedness theory of small BV weak solutions to a one-dimensional compressible Navier--Stokes model for reacting gas mixtures in dynamic combustion. The unknowns of the PDE system consist of the specific volume,…

Analysis of PDEs · Mathematics 2026-02-10 Siran Li , Haitao Wang , Jianing Yang

In this paper, we consider the 1D Navier-Stokes equations for viscous compressible and heat conducting fluids (i.e., the full Navier-Stokes equations). We get a unique global classical solution to the equations with large initial data and…

Analysis of PDEs · Mathematics 2011-03-09 Huanyao Wen , Changjiang Zhu

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

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 a dissipative quantum fluid on the whole space $\mathbb{R}^d$ ($d\geq 1$) confined by an external harmonic potential. The dynamics of the quantum fluid is described by the Quantum Navier-Stokes (QNS) system which is a particular…

Analysis of PDEs · Mathematics 2025-09-24 Jérémy Faupin , Ingrid Lacroix-Violet , Julien Lequeurre

The inhomogeneous incompressible Navier-Stokes equations with fractional Laplacian dissipations in the multi-dimensional whole space are considered. The existence and uniqueness of global strong solution with vacuum are established for…

Analysis of PDEs · Mathematics 2018-06-13 Dehua Wang , Zhuan Ye

We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical…

Analysis of PDEs · Mathematics 2018-05-23 Jan Brezina , Eduard Feireisl

We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an…

Analysis of PDEs · Mathematics 2015-11-17 Ondrej Kreml , Vaclav Macha , Sarka Necasova , Aneta Wroblewska-Kaminska