The Study On Incompressible Limit Of The Non-isentropic Magnetohydrodynamic Equations With Initial Boundary Value Problem

Magnetohydrodynamic(Magnetohydrodynamics(MHD)) is a combination of research methods of ?uid mechanics and electrodynamics, the conductive ?uid and electromagnetic interactions. In this paper, we use the classical energy method,Galerkin method, ?xed point theorem, trace theorem, regularity theory and continuum theory of magnetic ?uid dynamics asymptotic limit of the equations, we study the incompressible limit non compressible entropy MHD equations with initial boundary value problem under di?erent boundary conditions.In chapter 2, the velocity ?eld satis?es the Navier slip boundary conditions and to meet the perfect magnetic ?eld magnetic conduction conditions of MHD equation for small Mach number limit of bounded domain is studied. We have good initial value and The heat conduction conditions, using the energy method for?ne proved non compressible MHD equations to the entropy of the convergence of the solution of incompressible MHD equations. In the analysis process, we use some important inequalities, such as Gronwall inequality, Cauchy-Schwarz inequality, H¨older inequality, Hausdor?-Young inequality, the interpolation inequality, Sobolev embedding theorem.In chapter 3, we study the non isentropic MHD equations with initial boundary value problem on the half plane velocity ?eld for Dirichlet boundary conditions. We will adapt the ideal due to Valli to estimate higher-order derivatives by dividing it into the interior part and the part near the boundary, ?nally got the global existence and uniqueness of solutions of non compressible MHD equations of entropy, and the convergence of the incompressible MHD equations.In chapter 4, we study the problem of pressure limit is not available in the C4 with viscous polytropic ?uid has zero coe?cient of heat conduction boundary region of the compressible non isentropic MHD equations. In fact is the research area by the Dirichlet boundary problem of half plane to the general C4 bounded region. Compared with the third chapter of half plane, because it is the general area, usually on the boundary of derivative of higher order vector is not, so we need the high order derivative estimation to derive bounds on the introduction of the local area of the isothermal coordinates. In the initial conditions, the use of an important observation after coordinate transformation, we ?nished the processing on the boundary and the momentum equations containing1 large parameter elimination, resulting in a short period of time does not depend on the small Mach number ∈(0, 1] The consistent estimation, including estimation of high order derivative of velocity in the boundary normal vector direction.Magnetohydrodynamic(Magneto-Hydro-Dynamics, MHD) is an important branch of ?uid dynamics, and the many branches of physics,chemistry, metallurgy and nuclear power, Aerospace Science and technology have contact. Research on the MHD equations and the related model not only has the important theoretical signi?cance, And provide the important guarantee for scienti?c computing, so it has extensive application value.