We consider on the 2D torus the modified Surface Quasi-Geostrophic (mSQG) equation with [Formula: see text]-initial data and perturbed by multiplicative transport noise. Under a suitable scaling of the noises, we show that the solutions converge weakly to the unique solution of the dissipative mSQG equation.

中文翻译：

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具有乘性传输噪声的随机 mSQG 方程的缩放限制

我们在 2D 圆环上考虑修正的表面准地转 (mSQG) 方程，该方程具有 [公式：见文本] - 初始数据并受到乘性传输噪声的干扰。在适当的噪声缩放下，我们证明了这些解微弱地收敛到耗散 mSQG 方程的唯一解。