Lang Oana, Crisan Dan
Department of Mathematics, Imperial College London, London, SW7 2AZ UK.
Stoch Partial Differ Equ. 2023;11(2):433-480. doi: 10.1007/s40072-021-00233-7. Epub 2022 Jan 29.
We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the solution of the Euler equation with a family of viscous solutions which is proved to be relatively compact using a tightness criterion by Kurtz.
我们证明了具有输运型噪声的二维不可压缩流随机欧拉涡度方程存在唯一的全局强解。特别地，我们表明解的初始光滑性得以保持。论证基于用一族粘性解逼近欧拉方程的解，利用库尔茨的紧致性准则证明这族粘性解是相对紧致的。
