Non-unique weak solutions of forced SQG

Mimi Dai; Qirui Peng

Non-unique weak solutions of forced SQG

Analysis of PDEs 2023-10-23 v1

Authors: Mimi Dai , Qirui Peng

Abstract

We construct non-unique weak solutions $\theta\in C_t^0C_x^{0-}$ for forced surface quasi-geostrophic (SQG) equation. This is achieved through a convex integration scheme adapted to the sum-difference system of two distinct solutions. Without external forcing, non-unique weak solutions $\theta$ in space $C_t^0C_x^{\alpha}$ with $\alpha<-\frac15$ were constructed by Buckmaster, Shkoller and Vicol, and Isett and Ma.

Keywords

surface quasi-geostrophic equation non-unique weak solutions convex integration forced sqg sum-difference system

Cite

@article{arxiv.2310.13537,
  title  = {Non-unique weak solutions of forced SQG},
  author = {Mimi Dai and Qirui Peng},
  journal= {arXiv preprint arXiv:2310.13537},
  year   = {2023}
}

Comments

29 pages

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