| The main content of this paper is to study the global existence and decay estimate of solutions to two-dimensional magnetic-micropolar fluid equations with partial viscosity,and to study analyticity and time-decay rates of global solutions to three-dimensional generalized magnetohydrodynamics(MHD)equations near an equilibrium.This paper is divided into four chapters.The first chapter introduces the physical background and recall on some recent results on two-dimensional magneto-micropolar fluid equations with partial viscosity and three-dimensional generalized MHD equations near an equilibrium,respectively.The second chapter studies the global existence and time-decay rates of solutions to twodimensional magneto-micropolar fluid equations with partial viscosity.We prove the global existence of smooth large solutions by using energy method.In addition,we establish the optimal time-decay rates of global smooth large solutions by using the Fourier method.The third chapter studies the analyticity and time-decay rates of global mild solutions to the three-dimensional generalized MHD equations near an equilibrium.Using energy method in Fourier space method and the continuous argument,we establish global existence and analyticity of solutions in critical space.Then according to analyticity of global solutions,the time-decay rates is obtained.Finally,two-dimensional magnetic-micropolar fluid equations and three-dimensional generalized MHD equations are summarized and prospected in the fourth chapter. |
