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Strong ill-posedness
for SQG in critical Sobolev spaces
In-Jee Jeong and Junha Kim |
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Vol. 17 (2024), No. 1, 133–170
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Abstract |
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We prove that the inviscid surface quasigeostrophic (SQG) equations are strongly ill-posed in critical Sobolev spaces: there exists an initial data without any solutions in . Moreover, we prove strong critical norm inflation for -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 the two-dimensional incompressible Euler equations. |
Keywords
ill-posedness, norm inflation, critical space, surface
quasigeostrophic equation, fluid dynamics, nonexistence
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Mathematical Subject Classification
Primary: 35Q35, 76B47
Secondary: 35R25
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Milestones
Received: 8 September 2021
Revised: 17 March 2022
Accepted: 11 July 2022
Published: 5 February 2024
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Authors |
| In-Jee Jeong | |
| Department of Mathematical Sciences
and RIM Seoul National University Seoul South Korea |
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| Junha Kim | |
| School of Mathematics Korea Institute for Advanced Study Seoul South Korea |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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