12. John von Neumann Lecture: Prof. Dr. Camillo De Lellis (Universität Zürich): The Onsager's Theorem and beyond
Thursday, 11.01.2018 16:30 im Raum M5
In 1949 the famous physicist Lars Onsager made a quite striking statement about solutions of the incompressible Euler equations: if they are Hölder continuous for an exponent larger than 1/3, then they preserve the kinetic energy, whereas for exponents smaller than 1/3 there are solutions which do not preserve the energy. The first part of the statement has been rigorously proved by Peter Constantin, Weinan E and Endriss S. Titi in the nineties.
In a series of works László Székelyhidi and myself have introduced ideas from differential geometry and differential inclusions to construct nonconservative solutions and started a program to attack the other portion of the conjecture. After a series of partial results, due to a few authors, Phil Isett fully resolved the problem one year ago. However this has not stopped the growing of the subject, which affects several other equations of fluid dynamics and, perhaps most surprisingly, even the incompressible Navier-Stokes equations.