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SUMMARY:About wave and Schrödinger equations in the exterior of many stri
 ctly convex obstacles - David Lafontaine\, University of Bath
DTSTART:20190218T150000Z
DTEND:20190218T160000Z
UID:TALK119044@talks.cam.ac.uk
CONTACT:Ivan Moyano
DESCRIPTION:In order to study the non-linear Schrödinger and wave equatio
 ns\, it is crucial to understand the decay of solutions of the associated 
 linear equations. When a trapped trajectory exists\, a loss is unavoidable
  for a first family of a-priori estimates of the linear flow: the so-calle
 d smoothing estimates. In contrast\, we will show that in the exterior of 
 many strictly convex obstacles\, the estimates of space-time norms of solu
 tions\, known as Strichartz estimates\, hold with no loss with respect to 
 the flat case\, as soon as the dynamic of the trapped trajectories is suff
 iciently unstable. Finally\, if time permits\, we will say a word about th
 e associated non-linear equations: if the geometry does not induce too muc
 h concentration of energy\, we expect that the solutions behave linearly i
 n large times.
LOCATION:CMS\, MR13
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