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SUMMARY:Igor Rodnianski (Princeton)
DTSTART:20200512T200000Z
DTEND:20200512T210000Z
DTSTAMP:20260423T024512Z
UID:mitpde/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mitpde/4/">C
 ompressible fluids and singularity formation in supercritical defocusing S
 chrödinger equations</a>\nby Igor Rodnianski (Princeton) as part of MIT P
 DE/analysis seminar spring 2020\n\nLecture held in 2-135.\n\nAbstract\nWe 
 will discuss recent work with F. Merle\, P. Raphael and J. Szeftel\, where
  we studied\nthe problem of global regularity for a defocusing supercritic
 al Schrodinger equation. The\ncorresponding problem had been settled in th
 e affirmative in a long series of works in\nthe sub-critical and energy cr
 itical cases and was conjectured by J. Bourgain to have a\nsimilar positiv
 e answer in the supercritical case. We construct a set of smooth\, nicely\
 ndecaying initial data for which the corresponding solutions blow up in fi
 nite time with a\nhighly oscillatory behavior near singularity. The constr
 uction proceeds by establishing a\nlink between the Schr¨odinger and the 
 the compressible Euler equations. It also leads to\nnew singularity result
 s for the compressible Euler and Navier–Stokes equations.\n
LOCATION:https://researchseminars.org/talk/mitpde/4/
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