Name: Remark on the uniqueness of the mild solution of SQG equation
Keywords: 35Q35, 35Q86, Mathematics - Analysis of PDEs, quasi-geostrophic equation, mild solution, FOS: Mathematics, uniqueness, PDEs in connection with fluid mechanics, PDEs in connection with geophysics, Analysis of PDEs (math.AP)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 11 Sep 2024Embargo end date: 01 Jan 2023 English Publisher:Springer Science and Business Media LLCJournal:Partial Differential Equations and Applications, volume 5 (issn: 2662-2963, eissn: 2662-2971,

Authors: Iwabuchi, Tsukasa; Ueda, Ryoma;

doi: 10.1007/s42985-024-00301-2 , 10.48550/arxiv.2312.14337

arXiv: 2312.14337

Remark on the uniqueness of the mild solution of SQG equation

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Abstract

We study the two-dimensional surface quasi-geostrophic equation. Motivated by the uniqueness for the three-dimensional incompressible Navier-Stokes equations, we demonstrate that the uniqueness of the mild solution of the two-dimensional surface quasi-geostrophic equation holds in the scaling critical Lebesgue space with a unique structure of the non-linear term.

10 pages

Keywords

35Q35, 35Q86, Mathematics - Analysis of PDEs, quasi-geostrophic equation, mild solution, FOS: Mathematics, uniqueness, PDEs in connection with fluid mechanics, PDEs in connection with geophysics, Analysis of PDEs (math.AP)

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