Non-uniqueness up to the Onsager threshold for the forced SQG equation

Aynur Bulut; Manh Khang Huynh; Stan Palasek

Non-uniqueness up to the Onsager threshold for the forced SQG equation

Analysis of PDEs 2023-10-20 v1

Authors: Aynur Bulut , Manh Khang Huynh , Stan Palasek

Abstract

We establish new non-uniqueness results for the forced inviscid surface quasi-geostrophic equation, via an alternating formulation of convex integration techniques. Our results imply non-uniquenesss in the class of weak solutions with $|\nabla|^{-1}\theta\in C_tC_x^\alpha$ , for any $\alpha<1$ .

Keywords

surface quasi-geostrophic equation non-uniqueness weak solutions convex integration onsager threshold

Cite

@article{arxiv.2310.12947,
  title  = {Non-uniqueness up to the Onsager threshold for the forced SQG equation},
  author = {Aynur Bulut and Manh Khang Huynh and Stan Palasek},
  journal= {arXiv preprint arXiv:2310.12947},
  year   = {2023}
}

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22 pages

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