Global Well-posedness Of Two Types Of Magnetohydrodynamics Equations

This thesis focus on two types of magnetohydrodynamic equations,and studies the global existence and analyticity of mild soltion to the three-dimensional generalized incompressible Hall-magnetohydrodynamics system,and the global existence of classical solution to the incompressible 3D magneto-micropolar fluid equations with mixed partial viscosity near an equilibrium.This thesis is unfolded as four chapters,the first chapter introduces the background and research status of generalized incompressible Hall-magnetohydrodynamics system and magnetomicropolar fluid equations.For the case 1/2??,??1,the second chapter studies the three-dimensional generalized incompressible Hall-magnetohydrodynamics system.Using the energy estimate in Fourier space,we prove the global existence of solutions in critical space.Based on the global solutions,it is proved that the global solutions are analytical in this critical space by using the similar method.The third chapter investigates the initial value problem for the 3D magneto-micropolar fluid equations with mixed partial viscosity.The main purpose of this chapter is to establish global existence of classical small solutions.More precisely,we prove that the global stability of perturbations near the steady solution is given by a background magnetic field.The proof is mainly based on the energy estimate,the anisotropic interpolation inequality and the bootstrapping argument.In the last,the global well-posedness of two types of magnetohydrodynamics equations is summarized and prospected in the fourth chapter.