The Uniform Bound of the Viscosity of Incompressible Viscous Constantly Rotatinng Fluid

Abstract

The flow of incompressible viscous fluid is controlled by Navier-Stokes Equations.The qualititave analysis of the solutions of the equation is important to the studies of bifurcation problems and numerical solutions of the equations.In classic theory,it is held that, in Sobolev Space [H 1(Ω)] 3, there is the upper bound of the norm of the constant rotating flow of the incompressible viscous fluid between two closed surfaces. It is inversely proportional to the viscosity of the fluid, and it will go to infinity when the viscosity goes to zero. But in this paper, it is proven that the upper bound has nothing to do with the viscosity of the fluid by using decomposing theorems of spaces, Gauss's formula and Sobolev Space methods.