Global Well-posedness For 3D Inhomogeneous MHD Equations With Density-dependent Viscosity Coefficient

This thesis investigates the global well-posedness for the 3D magnetohydro-dynamic equations with density-dependent viscosity coefficients in the following form:Here,t>0 is time,and the unknown function P,?,u=(u1,u2,u3),and b ?(b1,b2,b3)denote the pressure,density,velocity,and magnetic field,respective-ly.D(u)?1/2[(?)u +((?)u)T]denotes the deformation tensor.?(?)and ?(?)stand for viscosity coefficients and satisfy the following bounded condition:(?)and(?)The N-S equation can be derived from the Boltzmann equation by some expan-sion.The viscosity coefficient is not a constant and depends on the temperature in this case.For isentropic flow,the viscosity depends on the density.Combining the Navier-Stokes equation with magnetic field,our model in this paper can be further established.This thesis mainly study the initial-boundary value problem of the MHD model(0.2)in vacuum case.By energy methods,we combine local exis-tence results with the estimates of unique local strong solution.Provided that ?(?)u0?L2 +?(?)b0?L2 is suitably small with arbitrary large initial density,contradicting the blow-up criteria,global-in-time unique strong solution can be obtained.