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 μâ†'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 μâ†'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.