Low Mach Number Limit To The 3D MHD Equations With The Insulating Boundary In A Bounded Domain

In this paper,we study the low Mach number limit problem for three-dimensional compressible MHD equations with the insulating boundary.On the boundary,the velocity field fulfills a Vorticity-Slip condition,while the magnetic field satisfies the insulating condition.We focus on constructing consistent estimates for global strong solutions in the small initial data.It is worth noting that due to the limitation of magnetic field boundary condition,its H2 estimation can not be obtained,so we use elliptic operator theory to estimate.Finally,when the Mach number approaches zero,we get the solution of the compressible MHD equations converges to the solution of the incompressible MHD equations.This paper presents the properties and conclusions of MHD equations in four parts:chapter 2 introduces the notations and the basic lemmas,for estimating Sobolev norms in bounded domains and dealing with boundary terms;Chapter 3 introduces L2 estimation,followed by lower order spatial,temporal or mixed derivatives,higher order derivatives.In order to overcome the difficulty of curl estimation due to the loss of the normal component,we construct the local coordinates by the isothermal coordinates to derive an estimate near the boundary.Next,we obtain consistent estimates for the Mach number ∈ and time t ∈[0,+∞),as well as the incompressible limit.Then,the H2 norm of magnetic field is estimated.Because the boundary condition of magnetic field is the insulating boundary condition,the higher order boundary term is difficult to deal with in energy estimation,so we use elliptic operator theory to estimate.Finally,It is about Prospects of low Mach number limit problems for 3D MHD equations with density.