Upper Bound Of Decay Rate For Solutions To The Navier-Stokes-Voigt Equations And The Approximation

Navier-Stokes-Voigt(abbreviated to NSV)equations,which describe the motion of a kind of viscoelastic incompressible fluid,are important nonlinear partial differential equations.There are many mathematicians and physicists pay much attention to these equations.This master dissertation mainly studies the decay rate of the weak solutions to the NSV equations and the approximation of the incompressible NSV equations by the artificial compressibility method.Firstly,we summarize the background of the NSV equations,as well as the known results related to the equations and the issues that we will address in this master dissertation.Then we investigate the upper bound of decay rate for the solutions to the NSV equations in R3.We first prove the well-posedness of the weak solutions for the NSV equations.Then we combine the Fourier splitting method of Schonbek to prove the upper bound of decay rate for the weak solutions.Finally,we study the approximation of the incompressible NSV equations by artificial compressibility method on three-dimensional bounded domains.We construct the “slight”compressible NSV equations,and prove that the weak solutions of the “slight”compressible NSV equations converge to the weak solutions of the incompressible NSV equations.