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SUMMARY:Resonances\, genericity and rational normal forms: The KillBill th
 eory - Erwan Faou (INRIA\, France)
DTSTART:20191028T150000Z
DTEND:20191028T160000Z
UID:TALK130465@talks.cam.ac.uk
CONTACT:pierre raphael
DESCRIPTION:Normal form theory has been succesfully used to analyze the lo
 ng time behavior of semi-linear PDEs on compact manifold. I will recall so
 me classical results and show how the presence of nonlinear resonances dri
 ves the stability of solutions for long times\, for smooth and small initi
 al data. I will then discuss two results: the case of waves equation in hi
 gh dimension\, and the completely resonant Schrödinger equation in 1D for
  which we can prove long time stability for « generic » initial data in 
 Sobolev space. This last result requires the use of rationnal normal forms
  conjugating the dynamics to an almost integrable one on some open set avo
 iding resonances. These are joint works with Joackim Bernier and Benoît G
 rébert. 
LOCATION:CMS\, MR13
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