Seminar Analysis: Giuseppe Genovese (University of Zurich)

Gibbs measures for the periodic derivative NLS equation

The DNLS equation is an integrable PDE, in the sense that there are infinitely many Hamiltonians associated to it. The aim of the talk is to present the construction of infinitely many functional measures associated to these integrals of motion of the equation, each measure being supported on Sobolev spaces of increasing regularity. These are natural candidates to be the invariant measures associated to the DNLS eq. Invariant measures are a crucial tool in the theory of integrable PDEs, useful e.g. to prove long time properties of regular solutions. The introductory general aspects will be reviewed and the new results on DNLS, obtained in collaboration with R. Luc (ICMAT,Madrid) and D. Valeri (MSC, Beijing), will be presented.

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