Seminar Analysis and Mathematical Physics: Elia Bruè (Institute for Advanced Study, Princeton)

Nonuniqueness results for the 2d Euler equations

A long-standing open question in fluid mechanics is whether the Yudovich uniqueness result for the 2d Euler system can be extended to the class of L^p-integrable vorticity. Recently, there have been formidable attempts to disprove this conjecture, none of which has by now fully solved it. I will outline two possible approaches to this problem. One is based on the convex integration technique introduced by De Lellis and Szekelyhidi. The second, proposed recently by Vishik, exploits the linear instability of certain stationary solutions.

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