Regularity Criteria For Tropical Climate System And Global Regularity For Magnetic Bénard Equations

In this thesis,we consider the regularity criteria for tropical climate systems.At the same time,we study the global regularity for magnetic Bénard equations in two dimension.This thesis is divided into four chapters.In chapter 1,we introduce the background of problems and main results of the thesis.In chapter 2,we introduce related preliminaries and lemmas of the thesis.In chapter 3,we study regularity criteria for tropical climate system in different situations.In two or three dimension,we will first show the regularity criteria in terms of ?v in Morrey-Campanato space.Then we will consider the regularity criterion in terms of v3 in the Lebesgue space.In chapter 4,we study global regularity for 2D magnetic Bénard equations with fractional dissipation,in which the dissipation terms are(-?)?u,(-?)?b and(-?)??,we will perform energy method to show the global regularity when 1<?<2,1/2<?<1,?=1 and ?+?? 2.