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

Siyu Liang

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

Analysis of PDEs 2022-11-11 v2 Probability

Authors: Siyu Liang

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).

Cite

@article{arxiv.2203.04655,
  title  = {On White Noise Solutions of mSQG Equations on $\mathbb{R}^{2}$},
  author = {Siyu Liang},
  journal= {arXiv preprint arXiv:2203.04655},
  year   = {2022}
}

Comments

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

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