Related papers: Global small solutions to 2-D incompressible MHD s…
In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a strong solution in the Lei-Lin space $\chi^{-1}(\mathbb{R}^2)$ with any initial data in…
This paper is concerned with the Cauchy problem of the two-dimensional MHD system with magnetic diffusion. It was proved that the MHD equations have a unique global strong solution around the equilibrium state $(0, e_1)$. Furthermore, the…
We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…
We introduce and investigate the wellposedness of two models describing the self-propelled motion of a "small bio-mimetic swimmer" in the 2D and 3D incompressible fluids modeled by the Navier-Stokes equations. It is assumed that the…
We study the two-dimensional generalized magnetohydrodynamics system with generalized dissipation and diffusion in terms of fractional Laplacians. It is known that the classical magnetohydrodynamics system with full Laplacians in both…
We consider an incompressible viscous flow without surface tension in a finite- depth domain of three dimension, with free top boundary. This system is governed by a Naiver-Stokes equation in a moving domain and a transport equation for the…
We study the magnetic two-component Hunter-Saxton system (M2HS), which was recently derived in \cite{M24} as a magnetic geodesic equation on an infinite-dimensional configuration space. While the geometric framework and the global weak flow…
This paper presents a new approach to the local well-posedness of the $1d$ compressible Navier-Stokes systems with rough initial data. Our approach is based on establishing some smoothing and Lipschitz-type estimates for the $1d$ parabolic…
We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time…
In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyze the problem corresponding to the Sobolev regularities $…
In this paper, we provide a much simplified proof of the main result in [Lin and Zhang, Comm. Pure Appl. Math.,67(2014), 531--580] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 3D…
In this paper, we consider the global well-posedness of the incompressible Hall-MHD equations in $\mathbb{R}^3$. We prove that the solution of this system is globally regular if the initial data is axisymmetric and the swirl components of…
We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space…
The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…
We prove short-time well-posedness and existence of global weak solutions of the Beris--Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous mixed Dirichlet and Neumann boundary conditions. The system…
This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in $\R^{N}$ with $N\geq2$. We address the question of well-posedness for {\it large} data having critical Besov regularity…
In this paper, we investigate the global existence of strong solutions for the inhomogeneous incompressible viscoelastic system with only velocity dissipation on $\mathbb{R}^{2}$. Due to the criticality of the time-weight, the methods for…
We prove the local well-posedness for the barotropic compressible Navier-Stokes system on a moving domain, a motion of which is determined by a given vector field ${\bf V}$, in a maximal $L_p-L_q$ regularity framework. Under additional…
In this paper we prove global well-posedness and modified scattering for the massive Maxwell-Klein-Gordon equation in the Coulomb gauge on $\mathbb{R}^{1+d}$ $(d \geq 4)$ for data with small critical Sobolev norm. This extends to the…
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…