Camillo De Lellis (Universität Zürich, Szwajcaria), From Nash to Onsager: funny coincidences across differential geometry and the theory of turbulence

Oddział Warszawski Polskiego Towarzystwa Matematycznego, Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego i Międzynarodowe Centrum Matematyczne im. Stefana Banacha

W dniu 9 stycznia 2014 roku (czwartek) o godzinie 14:15 w sali 3320 budynku Wydziału Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego przy ul. Banacha 2 (wejście od ul. Pasteura)
 

Prof. Camillo De Lellis ( Universität Zürich, Szwajcaria) -  mówca z ICM'2010, mówca plenarny z ECM'2012, laureat medalu Stampacchii 2009 i nagrody Fermata 2013

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FROM NASH TO ONSAGER: FUNNY COINCIDENCES ACROSS DIFFERENTIAL GEOMETRY AND THE THEORY OF TURBULENCE

Streszczenie wykładu:

Since the pioneering works of Scheffer and Shnirelman we know that Euler equations -- derived more than 250 years ago to describe the motion of an inviscid incompressible fluid -- have nontrivial solutions which are compactly supported in space and time. If they were to model the motion of a real fluid, we would see it suddenly start moving without any action of external forces.
Nash and Kuiper proved the existence of C¹ isometric embeddings of a fixed flat rectangle in arbitrarily small balls of R³. Thus, you should be able to put a fairly large piece of paper in a pocket of your jacket without folding or crumpling it. With Laszlo Szekelyhidi, we pointed out that these two counterintuitive facts share many similarities. This is even more apparent in our recent results, which prove the existence of Hӧlder continuous solutions that dissipate the kinetic energy. Our theorem might be regarded as a first step towards a conjecture of Lars Onsager, who in a 1949 paper about the theory of turbulence asserted the existence of such solutions for any Hӧlder exponent up to 1/3. The best result in this direction, 1/5, has been reached by Phil Isett.

                                                                                                                                                                                                                                                               Camillo De Lellis

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