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SUMMARY:Scattering and Smoothing for the Two-Dimensional Cubic Nonlinear S
 chrödinger Equation
DTSTART:20261028T130000Z
DTEND:20261028T140000Z
DTSTAMP:20261030T022300Z
UID:indico-event-17603@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Muyuan Lyu (Laboratoire de Mathématiques d'Orsay)\n
 \nSéminaire d'Analyse\nScattering theory describes the large-time behavio
 r of nonlinear evolution equations through comparison with a linear flow. 
 This raises a further question: can the nonlinear correction to the asympt
 otic state be smoother than the initial data?I will begin with an introduc
 tion to scattering for nonlinear Schrödinger equations\, highlighting sev
 eral developments that motivate this question. I will then present a deter
 ministic smoothing result for the two-dimensional cubic equation. Assuming
  that a solution scatters in the harmonic Sobolev space $(\\mathcal H^s)$\
 , with $(s>0)$\, the difference between its scattering state and its initi
 al datum belongs to $(\\mathcal H^{s+\\sigma})$ for every $(0<\\sigma<\\mi
 n{2s\,1})$. The proof combines the lens transform\, which turns the large-
 time problem into a finite-time endpoint problem\, with bilinear Strichart
 z estimates and harmonic spectral analysis. The emphasis will be on the me
 chanism behind the regularity gain.\n========\nPour être informé des pro
 chains séminaires vous pouvez vous abonner à la liste de diffusion en é
 crivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe 
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  laissez le corps du message vide.\n\nhttps://indico.math.cnrs.fr/event/17
 603/
LOCATION:Centre de conférences marilyn et James Simons (IHES)
URL:https://indico.math.cnrs.fr/event/17603/
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