Navier-Stokes方程外问题的粘性分离

Viscous Splitting for the Exterior Problem of Navier-Stokes Equations

用分步法求解N-S方程在无穷远处不为零的初边值外问题,证明了近似解与方程的解之差在空间L-(0,T;(H^(n+1)(Ω))~2),s<3/2是有界的,而且在空间L-(0,T,(H^1(Ω))~2)以O(k)的速率收敛,这里k是时间步长。

The viscous splitting for the exterior initial boundary problems of the Navier-Stokes equation whose solutions are nonzero at infinity is considered. It is proved that the differences of the apporimate solutions and the exact solutions are uniformly bounded in the space L∞(O, T; H5+1(Ω)), s<3/2; and converge with a rate of O(k) in the space L∞(O, T; H1(Ω)), where k is the length of time steps.