不可压粘性定常旋转流关于粘度的一致有界性

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

对于描述不可压缩粘性流体流动的 Navier- Stokes方程 ,其解的定性分析结果对于该方程的数值求解及其分歧问题的研究都是十分重要的 .经典理论认为 ,不可压缩粘性流体定常旋转流在Sobolev空间 [H1(Ω ) ]3中的范数的上界与流体粘度成反比 ,随着流体粘度的减小 ,这一上界会无限地增大 .文中利用空间分解定理、高斯公式及 Sobolev空间方法证明了不可压缩粘性流体定常旋转流在 Sobolev空间 [H 1(Ω ) ]3中存在一个与流体粘度无关的上界 .

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.