Existence And Decay Of Finite Energy Weak Solutions For Compressible Navier-Stokes Equations In 3D Bounded Domains

We study existence and decay of finite energy weak solutions for compressible Navier-Stokes equations in three-dimensional bounded domains,which read as follows:where t?0,x=(x1,x2,x3)??(?)R3,?=?(x,t)and u=(u1(x,t),u2(x,t),u3(x,t))represent,respectively,the density and the velocity,and the pressure P is associated with p.The full text is divided into five chapters,as follows:In Chapter 1,we briefly introduce the research background and research status of the Navier-Stokes equations,and give the main conclusions of this paper.In Chapter 2,we introduce some basic lemmas and commonly used symbols.In Chapter 3,by virtue of the Faedo-Galerkin approximation approach,we discuss the existence of finite energy weak solutions for compressible Navier-Stokes equations in three-dimensional bounded domains when P(?)satisfies certain conditions.In Chapter 4,basing on the existence of finite energy weak solutions and constructing the Lyapunov functional by the extra integrability of p,we obtain the exponential decay of finite energy weak solutions for compressible Navier-Stokes equations in three-dimensional bounded domains.In Chapter 5,we briefly summarize the content of this paper,and propose some problems that can be studied later.