论文标题
随机MSQG方程，带有乘法传输噪声：白噪声解决方案和缩放极限
Stochastic mSQG equations with multiplicative transport noises: white noise solutions and scaling limit
论文作者
论文摘要
我们考虑2D圆环$ \ mathbb {t}^2 $上的修改的表面准晶状体（MSQG）方程，并受到乘数传输噪声的扰动。该方程式在$ \ mathbb {t}^2 $上作为不变度度量的白噪声度量。我们首先通过点涡流近似的方法证明了随机方程的白噪声解，然后在噪声的合适缩放限制下，我们表明该溶液薄弱地趋于由时空白噪声驱动的耗散MSQG方程的独特固定溶液。后一个方程式的弱唯一性也通过遵循Gubinelli和Perkowski在\ cite {gp-18}中的方法来证明。
We consider the modified Surface Quasi-Geostrophic (mSQG) equation on the 2D torus $\mathbb{T}^2$, perturbed by multiplicative transport noise. The equation admits the white noise measure on $\mathbb{T}^2$ as the invariant measure. We first prove the existence of white noise solutions to the stochastic equation via the method of point vortex approximation, then, under a suitable scaling limit of the noise, we show that the solutions converge weakly to the unique stationary solution of the dissipative mSQG equation driven by space-time white noise. The weak uniqueness of the latter equation is also proved by following Gubinelli and Perkowski's approach in \cite{GP-18}.
