二维Euler-α方程的解收敛到欧拉方程组的解的简单证明

A Simple Proof of the Solution of two Dimensional Euler-α Equations Converge to the Solution of Euler Equations

令Euler-α方程的初始速度是欧拉方程极限的初速度的合适逼近。直接利用分部积分公式和插值不等式可证明得到,当α→0时,具Dirichlet边界条件的二维Euler-α方程组的解以L2空间及时间一致收敛于欧拉方程组的解。

Assume that the initial velocities for the Euler- α system approximate,in suitable sense,as the regularization parameter α → 0, the initial velocity for Euler system. Applying the interpolation inequalities and integration by parts, one can prove that the solutions of 2 D Euler- α in the Dirichlet converges to the one of Euler equations L2 in space and uniformly in time.