随机阻尼斯托克斯方程在$\mathbb R^d$中的定态解
Stationary solutions for stochastic damped Navier-Stokes equations in $\mathbb R^d$
摘要：
考虑$\mathbb R^d$（$d=2,3$）中的随机阻尼Navier-斯托克斯方程，假设噪声的协方差不太规则，因此Itô演算不能应用于有限能量向量场空间.我们证明了当$d=2$和$d=3$时不变测度和稳定解的存在性。
英文摘要：
We consider the stochastic damped Navier-Stokes equations in $\mathbb R^d$ ($d=2,3$), assuming as in our previous work [4] that the covariance of the noise is not too regular, so Itô calculus cannot be applied in the space of finite energy vector fields. We prove the existence of an invariant measure when $d=2$ and of a stationary solution when $d=3$.
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