粘性非等熵流体方程平衡解的稳定性

Stability for Stationary Solution of Non-Isentropic Viscous Fluid Equations

该文在三维空间中,研究Navier-Stokes-Poisson方程的平衡解及其非线性稳定性.当绝热指数4/3<γ<2时,利用约束变分的方法得到N-S-P方程的平衡解,并且证明该平衡解是非线性稳定的.当γ=4/3时,证明在一定条件下平衡解是不稳定的.

In three dimension space,we study the stationary solutions and nonlinear stability of Navier-Stokes-Poisson equations.Using variational method,we get the existence of stationary solution of N-S-P equations when 4/3〈 γ 〈2,the nonlinear stability of such steady states is also proved.As γ =4/3,we prove the nonlinear instability of stationary solution.