Global Solutions Of A Non-linear Parabolic System

This thesis is divided into four parts.The first part is the introduction which mainly introduces the research background,and some research results of the solution of NavierStokes equation.The second part lists the lemmas,definitions.The third part mainly derives the model equation and its local existence of solution.For the fourth part,we assume by contradiction that there is no global solution to the equation,and the local solution is found to be bounded by energy estimation and regularization enhancement.Then,the internal estimation also proves that the local solution is bounded.So the solution can be extended.We're going to find that the assumption is wrong.Thus it is proved that the equation has a global solution.