Related papers: Boundary layer expansions of the steady MHD equati…
As a continuation of \cite{LXY}, the paper aims to justify the high Reynolds numbers limit for the MHD system with Prandtl boundary layer expansion when no-slip boundary condition is imposed on velocity field and perfect conducting boundary…
In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0,…
In this paper, we consider the steady MHD equations with inhomogeneous boundary conditions for the velocity and the tangential component of the magnetic field. Using a new construction of the magnetic lifting, we obtain existence of weak…
In this paper, we validate the boundary layer theory for 2D steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0, L]\times\mathbb{R}_+\}$ under the assumption of a moving boundary at $\{Y=0\}$. The…
In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic (MHD) flow with no-slip boundary condition of velocity…
In this paper, we prove the global existence and the large time decay estimate of solutions to the two-dimensional MHD boundary layer equations with small initial data, which is analytical in the tangential variable. The main idea of the…
In this paper, we prove global existence of solutions with analytic regularity to the 2D MHD boundary layer equations in the mixed Prandtl and Hartmann regime derived by formal multi-scale expansion in \cite{GP}. The analysis shows that the…
We consider the validity of Prandtl boundary layer expansion of solutions to the initial boundary value problem for inhomogeneous incompressible magnetohydrodynamics (MHD) equations in the half plane when both viscosity and resistivity…
We study the two-dimensional MHD boundary layer equations. For small perturbation around a tangential background magnetic field, we obtain the global-in-time existence and uniqueness of solutions in Sobolev spaces. The proof relies on the…
In this paper, we are concerned with the magnetic effect on the Sobolev solvability of boundary layer equations for the 2D incompressible MHD system without resistivity. The MHD boundary layer is described by the Prandtl type equations…
In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics(MHD) equations, which are derived from the two dimensional density-dependent incompressible MHD equations.Under…
We consider a general compressible MHD system, where the magnetic field propagates in a heterogeneous medium. Using suitable penalization in terms of the transport coefficients we perform several singular limits. As a result we obtain: 1. A…
In this paper we consider the long time well-posedness of solutions to two dimensional compressible magnetohydrodynamics (MHD) boundary layer equations. When the initial data is a small perturbation of a steady solution with size of…
This paper is concerned with the validity of the Prandtl boundary layer theory in the inviscid limit of the steady incompressible Navier-Stokes equations, which is an extension of the pioneer paper (Y. Guo et al., 2017, Ann. PDE) from a…
In this paper, we investigate the similarity solutions for a steady laminar incompressible boundary layer equations governing the Magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies.…
In this paper, we investigate the convergence rates of inviscid limits for the free-boundary problems of the incompressible magnetohydrodynamics (MHD) with or without surface tension in $\mathbb{R}^3$, where the magnetic field is…
In this paper, we obtain the global-in-$x$ Sobolev stability of Prandtl layer expansions for 2-D steady incompressible MHD flows with shear outer ideal MHD flows $(1,0,\sigma,0)$ ($\sigma\geq 0$) on a moving plate. It is worth noticing that…
We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that if the magnetic field and velocity field are never…
This paper is concerned with the vanishing viscosity and magnetic resistivity limit for the two-dimensional steady incompressible MHD system on the half plane with no-slip boundary condition on velocity field and perfectly conducting wall…
In this paper, we we study boundary layer problems for the incompressible MHD systems in the presence of physical boundaries with the standard Dirichlet oundary conditions with small generic viscosity and diffusion coefficients. We identify…