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arXiv · 2107.07739

Strong illposedness for SQG in critical Sobolev spaces

In-Jee Jeong·Junha Kim
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Abstract

We prove that the inviscid surface quasi-geostrophic (SQG) equations are strongly ill-posed in critical Sobolev spaces: there exists an initial data $H^{2}(\bbT^2)$ without any solutions in $L^\infty_{t}H^{2}$. Moreover, we prove strong critical norm inflation for $C^\infty$--smooth data. Our proof is robust and extends to give similar ill-posedness results for the family of modified SQG equations which interpolate the SQG with two-dimensional incompressible Euler equations.

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In-Jee Jeong, Junha Kim. 2021-07-16. Strong illposedness for SQG in critical Sobolev spaces. https://doi.org/10.2140/apde.2024.17.133

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