| In this paper,we mainly study the existence,analyticity and time decay rate of the global solutions of the magnetohydrodynamics equations with Coriolis forces and their related models.Specifically,when the initial values are near an equilibrium,this paper mainly uses the energy method,frequency division technique and continuous argument method in Fourier space to study the existence and analytic properties of the global solution to the initial value problem of the MHD equations with Coriolis force,and the existence,analyticity and time decay rate of the global solution to the initial value problem of the generalized Hall MHD equations.This paper is divided into four chapters.The first chapter mainly introduces the physical background,research status and main research content of the magnetohydrodynamic equations with Coriolis force and Hall magnetohydrodynamic equations,and gives the preparatory knowledge.In Chapter 2,the existence and analyzability of global solutions to the initial value problems of magnetohydrodynamic equations with Coriolis forces are studied.First,when the two parameters are equal and the initial values are near an equilibrium,the existence and analyzability of the global solution of the initial value problem and the existence of a special global solution are proved.Secondly,when the two parameters are not equal and the initial values are near an equilibrium,the existence and analyzability of the global solution of the initial value problem of the equations are proved.In Chapter 3,the existence,analytic property and time decay rate of the global solution of the initial value problem of the generalized Hall magnetohydrodynamic equations are studied.When the initial values are near an equilibrium,the existence,analytic property and time decay rate of the global solution of the initial value problem of the equations are proved.In the last chapter,the main research content of this paper is summarized and prospected. |
