We prove existence and uniqueness of martingale solutions to a (slightly) hyper-viscous stochastic Navier–Stokes equation in 2d with initial conditions absolutely continuous with respect to the Gibbs measure associated to the energy, getting the results both in the torus and in the whole space setting.

中文翻译：

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具有白噪声不变测度的高粘性随机 Navier-Stokes 方程

我们证明了 2d 中（略微）超粘性随机 Navier-Stokes 方程的鞅解的存在性和唯一性，初始条件相对于与能量相关的吉布斯测度绝对连续，在环面和整体中都得到了结果空间设置。