The Viscosity-limit, The Existence Of The General Solutions Of Initial Problem And The Steady-state Solutions Of The Incompressible N-S Equations

In this paper, we discuss the viscosity-limit, the existence of the general solution-s of initial problem and the steady-state solutions of the incompressible Navier-Stokesequations,Firstly, we discuss the viscosity-limit of Navier-Stokes equations in R2. The strongsolution converge to the weak solution of Euler equations when viscous coefcient μ→0.If the solution of2D Euler equations is exist, then the strong solution of Navier-Stokesequations strong convergence to the solution of Euler equations, when μ→0.Secondly, we discuss the initial problem of Navier-Stokes equations in R3, we put thisequations convert to integral equations, prove the existence of the initial solution of theNavier-Stokes equations with fxed point lemma of bilinear forms.Thirdly, we concern with three dimensional steady-state Navier-Stokes equations withminimal external force, by control the kinematic viscosity, we prove the existence of thesteady-state solutions with fxed point lemma of bilinear forms.