Related papers: Global well-posedness for axisymmetric MHD system …
The purpose of this paper is to study the incompressible non-resistive MHD equations in $\mathbb{R}^3$. We establish the global well-posedness of classical solutions if the initial data is axially symmetric and the swirl components of the…
In this paper, we are concerned with the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity when the initial velocity is sufficiently small in the critical Besov space…
We consider three dimensional incompressible Navier-Stokes equation $(NS)$ with different viscous coefficient in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared to the…
This paper concerns the initial boundary value problem of three-dimensional inhomogeneous incompressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficient $\mu(\rho)$ is a power function of the density…
In this paper, we investigate the global existence of weak solutions to 3-D inhomogeneous incompressible MHD equations with variable viscosity and resistivity, which is sufficiently close to $1$ in $L^\infty(\mathbb{R}^3),$ provided that…
This paper investigates the stabilization effect of a background magnetic vorticity on electrically conducting fluids. By exploring the dissipation nature of the linearized equations, we prove the global existence of smooth solutions to the…
We obtain the global well-posedness to the 3D incompressible magnetohydrodynamics (MHD) equations in Besov space with negative index of regularity. Particularly, we can get the global solutions for a new class of large initial data. As a…
This paper studies the Cauchy problem for three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic equations with vacuum as far field density. We prove the global existence and uniqueness of strong solutions provided…
We revisit the global existence of solutions with some large perturbations to the incompressible, viscous, and non-resistive MHD system in a three-dimensional periodic domain, where the impressed magnetic field satisfies the Diophantine…
The small data global well-posedness of the 3D incompressible Navier-Stokes equations in $\mathbb R^3$ with only one-directional dissipation remains an outstanding open problem. The dissipation in just one direction, say $\partial_1^2 u$ is…
This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a…
In this paper, we obtain the low order global well-posedness and the asymptotic behavior of solution of 2D MHD problem with partial dissipation in half space with non-slip boundary condition. When magnetic field equal zero, the system be…
We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field.…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that…
We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken…
We study in this paper the axisymmetric 3-D Navier-Stokes system where the horizontal viscosity is zero. We prove the existence of a unique global solution to the system with initial data of Yudovitch type
This paper establishes the global well-posedness of solutions to the Oldroyd-B model with purely horizontal viscosity and arbitrarily large initial data in two-dimensional settings, including the full space $\mathbb{R}^2$, the partially…
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…
We consider a viscous incompressible fluid below the air and above a fixed bottom. The fluid dynamics is governed by the gravity-driven incompressible Navier-Stokes equations, and the effect of surface tension is neglected on the free…