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SUMMARY:Invariant measures for some Hamiltonian PDEs - Tadahiro Oh (Prince
 ton)
DTSTART:20111101T150000Z
DTEND:20111101T160000Z
UID:TALK34088@talks.cam.ac.uk
CONTACT:Jonathan Ben-Artzi
DESCRIPTION:In this talk\, we discuss ideas and results related to invaria
 nt Gibbs measures and white noise for some Hamiltonian PDEs. First\, we br
 iefly discuss the construction of Gibb measures\, and then review Bourgain
 's idea for extending local-in-time solutions to global ones almost surely
  with respect to such Gibbs measures. The main idea is to use invariance o
 f finite dimensional Gibbs measures as a replacement of conservation laws.
  In the second part\, we will describe almost sure local and global well-p
 osedness of 1-d (Wick ordered) cubic NLS below L^2. This can be viewed as 
 a first step toward proving invariance of the white noise.
LOCATION:CMS\, MR14
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