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. As a main novelty, 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.

我们研究了受随机强迫的三维不可压缩欧拉方程。我们开发了耗散鞅解的概念，其中非线性项由广义杨氏测度描述。我们将这些解构造为相应随机 Navier-Stokes 方程解的消失粘度极限。这需要结合广义杨氏测度的改进的随机紧致方法。作为一个主要的新颖之处，我们的解决方案满足了一种形式的能量不等式，这会产生一个弱-强唯一性结果（路径和法律）。一旦强解存在，耗散鞅解就与强解重合（路径上或在法律上）。