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We are concerned with the global existence of finite energy weak solutions to 3D density-dependent magnetohydrodynamics (MHD) system with Hall-effect set in a general smooth bounded domain. The perfectly conducting wall boundary condition…

Analysis of PDEs · Mathematics 2021-09-01 Jin Tan

We consider the strong and weak solutions to the Cauchy problem of the inhomogeneous incompressible nematic liquid crystal equations in two dimensions. We first establish the local existence and uniqueness of strong solutions by using the…

Analysis of PDEs · Mathematics 2015-03-13 Jinkai Li

In this paper we consider the Quantum Navier-Stokes system both in two and in three space dimensions and prove global existence of finite energy weak solutions for large initial data. In particular, the notion of weak solutions is the…

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

In this paper we prove global in time existence of weak solutions to zero Mach number systems arising in fluid mechanics. Relaxing a certain algebraic constraint between the viscosity and the conductivity introduced in [D. Bresch, E.H.…

Analysis of PDEs · Mathematics 2015-03-19 Didier Bresch , Vincent Giovangigli , Ewelina Zatorska

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…

Analysis of PDEs · Mathematics 2026-01-13 Bohan Ouyang , Maurizio Grasselli , Hao Wu

We prove global existence and modified scattering property for the solutions of the $2D$ gravity water waves system in the infinite depth setting for a class of initial data, which is only required to be small above the level…

Analysis of PDEs · Mathematics 2016-11-17 Xuecheng Wang

In this paper, we prove that the existence of globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking. We first introduce a new set of independent and dependent variables in…

Analysis of PDEs · Mathematics 2024-09-30 Yonghui Zhou , Xiaowan Li

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…

Analysis of PDEs · Mathematics 2015-06-03 Helmut Abels , Daniel Depner , Harald Garcke

The dynamics of multicomponent gas mixtures with vanishing barycentric velocity is described by Maxwell-Stefan equations with mass diffusion and heat conduction. The equations consist of the mass and energy balances, coupled to an algebraic…

Analysis of PDEs · Mathematics 2023-04-03 Stefanos Georgiadis , Ansgar Jüngel

The principle purpose of this work is to investigate a "viscous" version of a "simple" but still realistic bi-fluid model described in [Bresch, Desjardin, Ghidaglia, Grenier, Hillairet] whose "non-viscous" version is derived from physical…

Analysis of PDEs · Mathematics 2019-09-04 Antonin Novotny , Milan Pokorny

We prove the global existence of weak solution for two dimensional Ericksen-Leslie system with the Leslie stress and general Ericksen stress under the physical constrains on the Leslie coefficients. We also prove the local well-posedness of…

Analysis of PDEs · Mathematics 2013-06-05 Meng Wang , Wendong Wang

This paper studies the Cauchy problem of the incompressible magnetohydrodynamic systems with or without viscosity $\nu$. Under the assumption that the initial velocity field and the displacement of the initial magnetic field from a non-zero…

Analysis of PDEs · Mathematics 2016-05-03 Yuan Cai , Zhen Lei

This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain.…

Analysis of PDEs · Mathematics 2015-04-07 Scott Smith

We investigate global well-posedness to the Cauchy problem of three-dimensional compressible viscous and heat-conducting micropolar fluid equations with zero density at infinity. By delicate energy estimates, we establish global existence…

Analysis of PDEs · Mathematics 2022-03-15 Yang Liu , Xin Zhong

We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In view of Taylor's conjecture, this proves that there exist…

Analysis of PDEs · Mathematics 2019-07-25 Rajendra Beekie , Tristan Buckmaster , Vlad Vicol

We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of…

Analysis of PDEs · Mathematics 2009-11-07 Michael Kunzinger , Gerhard Rein , Roland Steinbauer , Gerald Teschl

This work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\geq 2$ in…

Analysis of PDEs · Mathematics 2011-10-28 Boris Haspot

Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…

Analysis of PDEs · Mathematics 2026-02-05 Huangxin Chen , Jisheng Kou , Haitao Leng , Shuyu Sun , Hai Zhao

The existence of global-in-time classical solutions to the Cauchy problem of compressible magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linear structure is a degenerated hyperbolic-parabolic…

Analysis of PDEs · Mathematics 2014-05-05 Xianpeng Hu

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