Ill-posedness of the Euler equations in the critical Sobolev space

Ill-posedness of the Euler equations in the critical Sobolev space

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In-Jee Jeong, Princeton University
Fine Hall 322

The question of well-posedness of the Euler equations in various critical spaces was only recently solved. Ill-posedness in the critical Sobolev spaces was obtained by Bourgain-Li, and ill-posedness in the integer C^m spaces was settled again by Bourgain-Li and independently by Elgindi-Masmoudi.  In this talk, we give a simple proof of the ill-posedness in the critical Sobolev space for the 2D Euler equations. The proof is based on a hyperbolic flow scenario, utilized in the recent works of Denissov, Kiselev-Sverak, and Zlatos. This is joint work with Tarek Elgindi.