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

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).