English
Related papers

Related papers: Weak-strong uniqueness property for models of comp…

200 papers

We consider the two-dimensional incompressible inhomogeneous Navier-Stokes equations with odd viscosity, where the shear and the odd viscosity coefficients depend continuously on the unknown density function. We establish the existence of…

Analysis of PDEs · Mathematics 2025-08-26 Rebekka Zimmermann

We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…

Analysis of PDEs · Mathematics 2025-08-26 Piotr B. Mucha , Sarka Necasova , Maja Szlenk

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

The existence and uniqueness of the local strong solution to the three-dimensional compressible viscoelastic fluids near the equilibrium is established. In addition to the uniform estimates on the velocity, some essential uniform estimates…

Analysis of PDEs · Mathematics 2010-01-21 Xianpeng Hu , Dehua Wang

We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. We derive the relative entropy inequality in the spirit of…

Analysis of PDEs · Mathematics 2016-06-16 Ondřej Kreml , Šárka Nečasová , Tomasz Piasecki

In this work we employ the relative energy method to obtain a weak-strong uniqueness principle for a Euler-Riesz system, as well as to establish its convergence in the high-friction limit towards a gradient flow equation. The main technical…

Analysis of PDEs · Mathematics 2024-07-09 Nuno J. Alves , José A. Carrillo , Young-Pil Choi

We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a…

Analysis of PDEs · Mathematics 2022-08-05 Nilasis Chaudhuri , Eduard Feireisl , Ewelina Zatorska

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…

Analysis of PDEs · Mathematics 2017-01-03 Helmut Abels , Dominic Breit

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 are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and that the initial…

Analysis of PDEs · Mathematics 2020-01-08 Raphaël Danchin , Francesco Fanelli , Marius Paicu

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

In this paper, we considered the isentropic Navier-Stokes equations for compressible fluids with density-dependent viscosities in $\mathbb{R}^3$. These systems come from the Boltzmann equations through the Chapman-Enskog expansion to the…

Analysis of PDEs · Mathematics 2015-03-20 Shengguo Zhu

In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. In contrast…

Analysis of PDEs · Mathematics 2021-03-30 Paolo Antonelli , Stefano Spirito

This paper is dedicated to the global existence of entropy weak solutions for the Poisson-Nernst-Planck-Compressible Navier-Stokes system in a periodic domain $\Pi$ d when the shear viscosity $\mu$($\rho$) = $\mu$ $\rho$ with $\mu$ to be…

Analysis of PDEs · Mathematics 2026-03-13 Didier Bresch , Maria Kazakova , Charlotte Tonnelier

This paper addresses the weak-strong uniqueness property and singular limit for the compressible Primitive Equations (PE). We show that a weak solution coincides with the strong solution emanating from the same initial data. On the other…

Analysis of PDEs · Mathematics 2020-02-03 Hongjun Gao , Sarka Necasova , Tong Tang

We prove uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We make use of the Lagrangean framework in comparing the instantaneous states of corresponding fluid particles in two…

Analysis of PDEs · Mathematics 2020-12-15 Anthony Suen

Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are…

Analysis of PDEs · Mathematics 2009-04-24 Ning Jiang , C. David Levermore

In a three-dimensional bounded domain $\Omega$ we consider the compressible Navier-Stokes equations for a barotropic fluid with general non-linear density dependent viscosities and no-slip boundary conditions. A nonlinear drag term is added…

Analysis of PDEs · Mathematics 2025-02-11 Luca Bisconti , Matteo Caggio , Filippo Dell'Oro

We study the barotropic compressible Navier-Stokes system where the shear viscosity is a positive constant and the bulk one proportional to a power of the density with the power bigger than one and a third. The system is subject to the…

Analysis of PDEs · Mathematics 2022-06-01 Xinyu Fan , Jiaxu Li , Jing Li

We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…

Analysis of PDEs · Mathematics 2022-02-23 Lorena Bociu , Boris Muha , Justin T. Webster