Well-posedness Of The Solutions To Two Kinds Of Fluid Equations

In this thesis,we focus on the well-posedness of the solutions to two kinds of fluid equations.In chapter 1,we introduce the research background and current research status of the generalized MHD equations and the hyperbolic balance law system,and gives our main results of this paper.In chapter 2,we review some important inequalities,then the definition of invariant region and theorem are introduced.In chapter 3,we mainly study the generalized MHD equations in 2 dimensional:(?) L2? is defined as(?),(?),q:R+?R+.When 0<?<1/2,?>1,3?+2?>3,u0,b0?Hs(R2),s?2,we proved that the solutions(u,b)are globally regular.In chapter 4,we study the global regularity of the hyperbolic balance law system.The existence of viscous solutions of a hyperbolic balance law is established.Then,by using the natural entropy of the system,some higher order estimates of viscosity solutions are obtained.