定常Navier-Stokes方程解集的结构

Solution Set structure for Stationary Navier-Stokes Equations

本文将Navier-Stokes方程化为一个非线性算子方程进行讨论,首先我们研究了解的整体性态,从而证明了过原点(λ,u)=(0,θ)的连通分支一定通向λ=+∞.进一步讨论了在简单特征值的情形下,解在某一子空间上无分歧.

We transform the stationary Navier-Stokes equations into a nonlinear operator equation,by which the global behaviour of the solution set is studied.It is proved that the continuous solution component passing through original point (λ,u)=(0,θ) extends to λ=+∞.Furthermore,given the condition that all the eigenvalues are simple.We prove that the solution set has no bifurcation in certain subspace.