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SUMMARY:Alex Barron (UIUC)
DTSTART:20210405T210000Z
DTEND:20210405T220000Z
DTSTAMP:20260423T005716Z
UID:OARS/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/20/">A 
 sharp global-in-time Strichartz estimate for the Schrodinger equation on t
 he infinite cylinder</a>\nby Alex Barron (UIUC) as part of OARS Online Ana
 lysis Research Seminar\n\n\nAbstract\nThe classical Strichartz estimates s
 how that a solution to the linear Schrodinger equation on Euclidean space 
 is in certain Lebesgue spaces globally in time provided the initial data i
 s in L^2. On compact manifolds one can no longer have global control\, and
  some loss of derivatives is necessary in interesting cases (meaning the i
 nitial data needs to be in a Sobolev space rather than L^2). On non-compac
 t manifolds it is a challenging problem to understand when one can have go
 od space-time estimates with no loss of derivatives. \n\nIn this talk we d
 iscuss an endpoint Strichartz-type estimate for the linear Schrodinger equ
 ation on the infinite cylinder (or\, equivalently\, with one periodic comp
 onent and one Euclidean component). Our estimate is sharp\, scale-invarian
 t\, and requires only L^2 data. This contrasts the purely periodic case wh
 ere some loss of derivatives is necessary at the endpoint\, as originally 
 observed by Bourgain.\n\nJoint work with M. Christ and B. Pausader.\n
LOCATION:https://researchseminars.org/talk/OARS/20/
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