English
Related papers

Related papers: Global weak solutions to compressible quantum Navi…

200 papers

We investigate the barotropic compressible Navier-Stokes equations with the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial density that is allowed to vanish, we establish the global…

Analysis of PDEs · Mathematics 2025-07-04 Qinghao Lei , Chengfeng Xiong

We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…

Analysis of PDEs · Mathematics 2013-05-27 Song Jiang , Chunhui Zhou

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 investigate the inertial limit of the compressible Navier--Stokes system posed on the $3$-dimensional torus, and allowing for regions of vacuum. Considering global-in-time finite-energy weak solutions of a scaled system, we rigorously…

Analysis of PDEs · Mathematics 2026-03-13 Cheng Yu

A fluid-particle system of the inhomogeneous Navier-Stokes equations and Vlasov equation in the three dimensional space is considered in this paper. The coupling arises from the drag force in the fluid equations and the acceleration in the…

Analysis of PDEs · Mathematics 2013-04-18 Dehua Wang , Cheng Yu

We are concerned with the compressible barotropic Navier--Stokes equations for a $\gamma$-law gas with density-dependent bulk viscosity coefficient $\lambda=\lambda(\rho)=\rho^\beta$ on the two-dimensional periodic domain $\mathbb{T}^2$.…

Analysis of PDEs · Mathematics 2025-07-01 Siran Li , Jianing Yang

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

For periodic initial data with initial density allowed to vanish, we establish the global existence of strong and weak solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data…

Analysis of PDEs · Mathematics 2012-06-19 Xiangdi Huang , Jing Li

In this paper, we study a coupled compressible Navier-Stokes/Q-tensor system modeling the nematic liquid crystal flow in a three-dimensional bounded spatial domain. The existence and long time dynamics of globally defined weak solutions for…

Analysis of PDEs · Mathematics 2013-07-30 Dehua Wang , Xiang Xu , Cheng Yu

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak…

Analysis of PDEs · Mathematics 2015-04-01 Eduard Feireisl , Ondřej Kreml , Šárka Nečasová , Jiří Neustupa , Jan Stebel

This work is devoted to the global existence of weak solution for a general isothermal model of capillary fluids derived by C. Rohde, which can be used as a phase transition model. This article is structured in the following way: first of…

Analysis of PDEs · Mathematics 2008-03-14 Boris Haspot

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

In this paper, we study the global well-posedness of a coupled system of kinetic and fluid equations. More precisely, we establish the global existence of weak solutions for Navier-Stokes-BGK system consisting of the BGK model of Boltzmann…

Analysis of PDEs · Mathematics 2018-01-26 Young-Pil Choi , Seok-Bae Yun

In this paper, we shall prove the global existence of weak solutions to 3D inhomogeneous incompressible Navier-Stokes system $({\rm INS})$ with initial density in the bounded function space and having a positive lower bound and with initial…

Analysis of PDEs · Mathematics 2018-06-12 Ping Zhang

We prove global existence of appropriate weak solutions for the compressible Navier--Stokes equations for more general stress tensor than those covered by P.-L. Lions and E. Feireisl's theory. More precisely we focus on more general…

Analysis of PDEs · Mathematics 2016-02-08 Didier Bresch , Pierre-Emmanuel Jabin

We consider a compressible Navier-Stokes system for a barotropic fluid with density dependent viscosity in a three-dimensional time-space domain $(0,T)\times \Omega_\varepsilon$ where $\Omega_\varepsilon = (0,\varepsilon)^2\times (0,1)$. We…

Analysis of PDEs · Mathematics 2020-08-25 Matteo Caggio , Vaclav Macha

This paper considers the degenerate and singular chemotaxis-Navier--Stokes system with logistic term $n_t + u\cdot\nabla n =\Delta n^m - \chi\nabla\cdot(n\nabla c) + \kappa n -\mu n^2$, $x \in \Omega,\ t>0$, $c_t + u\cdot\nabla c = \Delta c…

Analysis of PDEs · Mathematics 2018-02-27 Shunsuke Kurima , Masaaki Mizukami

We obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of data allowing growth at spatial infinity. Namely, we show the global existence of suitable weak solutions when the initial data…

Analysis of PDEs · Mathematics 2020-01-08 Zachary Bradshaw , Igor Kukavica , Tai-Peng Tsai

In this paper, we consider the quantum MHD equations with both the viscosity coefficient and the magnetic diffusion coefficient are depend on the density. we prove the global existence of weak solutions and perform the lower planck limit in…

Analysis of PDEs · Mathematics 2018-05-08 Hao Li , Yachun Li

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