论文标题
随机欧拉方程的耗散解决方案
Dissipative solutions to the stochastic Euler equations
论文作者
论文摘要
我们研究了受随机强迫的三维不可压缩的Euler方程。我们开发了一个耗散性的martingale解决方案的概念，其中非线性术语通过广义的年轻措施描述。我们将这些解决方案构建为解决方案的消失粘度极限对相应的随机Navier-Stokes方程。这需要一种结合了广义的年轻措施的精致随机紧凑方法。我们的解决方案满足了能量不平等的形式，从而产生了弱的唯一性结果（路线和法律）。一旦存在，耗散性的martingale解决方案（路径或法律）与强大的解决方案一致。
We study the three-dimensional incompressible Euler equations subject to stochastic forcing. We develop a concept of dissipative martingale solutions, where the nonlinear terms are described by generalised Young measures. We construct these solutions as the vanishing viscosity limit of solutions to the corresponding stochastic Navier-Stokes equations. This requires a refined stochastic compactness method incorporating the generalised Young measures. Our solutions satisfy a form of the energy inequality which gives rise to a weak-strong uniqueness result (pathwise and in law). A dissipative martingale solution coincides (pathwise or in law) with the strong solution as soon as the latter exists.
