On White Noise Solutions of mSQG Equations on $\mathbb{R}^{2}$

Siyu Liang

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arXiv · 2203.04655

On White Noise Solutions of mSQG Equations on $\mathbb{R}^{2}$

Siyu Liang

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Abstract

In this paper, we show existence of white noise solutions for weak formulations of modified Surface Quasi-Geostrophic (mSQG) equations. Based on previous results (\cite{FS}) on white noise solutions for mSQG equations on the torus $\mathbb{T}^{2}$, we show a similar result for the whole space $\mathbb{R}^{2}$ by letting the volume of the torus go to infinity and applying compactness methods (Skorokhod's theorem).

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Siyu Liang. 2022-03-09. On White Noise Solutions of mSQG Equations on $\mathbb{R}^{2}$. https://arxiv.org/abs/2203.04655

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