Speaker: In-Jee Jeong 教授 韩国高等研究院（KIAS）
Inviter: 秦国林 博士
Title: Illposedness for incompressible fluid models at critical Sobolev regularity (2)
Language: English
Time & Venue: 2026.03.19 16:00-17:00 南楼202
Abstract: For the incompressible Euler equation, critical Sobolev spaces are characterized by having the same scaling with the Lipschitz norm of the velocity. While local wellposedness for subcritical Sobolev spaces is classical, illposedness in critical and supercritical cases was obtained only relatively recently, starting with the pioneering works of Bourgain-Li and Elgindi-Masmoudi in 2014. We briefly review historical developments on this illposedness problem. Then we discuss a recent proof strategy based on the Hardy inequality and ``Key Lemma'' of Kiselev and Sverak, using vorticities having the form of "dyadic bubbles." This robust strategy allows us to obtain strong, quantitative illposedness results in various Sobolev spaces without any contradiction arguments, and can be extended several other models, including the (generalized) SQG equations. Based on joint works with Junha Kim.
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