Well-posedness And Decay Of Solution To The Three Dimensional Generalized Navier-stokes Equations With Damping

In this paper,the generalized Navier-Stokes equations with damping are consid-ered.We will show that the generalized Navier-Stokes equations with damping |u|?-1u have weak solutions for any ?>1 and 0<?<5/4.In addition we will use the Fourier splitting method to prove the L2 decay of weak solutions for ?>2 and 0<?<3/4.This dissertation is divided into four chapters.The main research results are outlined as follows:Chapter One introduces the history of the three dimensional generalized Navier-Stokes equations with damping.In Section two,we outlines the actuality for the study of the three dimensional generalized Navier-Stokes equations with damping.Chapter Two firstly we give the basic function space Lp(?)space and Sobolev space.In the second section,some inequalities used in the research process are given.In Chapter Three,we introduce the definition of the weak solution of the classical Navier-Stokes equations and the definition of the weak solution of the three dimen-sional generalized Navier-Stokes equations with damping terms in the first section.In the second section,we give the Aubin-Lions lemma,Plancherel theorem and auxiliary functions constructed.In Chapter Four,well-posedness of three dimensional generalized Navier-Stokes equations with damping are considered by Galerkin approximation method in the first section,uses classical Fourier splitting method to obtain the decay of weak solutions in the second section.