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).

arXiv commentAccepted by JMAA with the following link: https://www.sciencedirect.com/science/article/abs/pii/S0022247X22008447