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SUMMARY:Steve Shkoller (University of California\, Davis)
DTSTART:20200723T150000Z
DTEND:20200723T155000Z
DTSTAMP:20260423T035631Z
UID:IMS/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/45/">Sho
 ck Formation for the 3d Euler Equations</a>\nby Steve Shkoller (University
  of California\, Davis) as part of PDE seminar via Zoom\n\n\nAbstract\nTog
 ether with Tristan Buckmaster and Vlad Vicol\, we give a constructive proo
 f of the shock formation process for the 3d Euler equations with vorticity
 .  Specifically\, we prove that there exist smooth solutions which form a 
 generic stable shock with explicitly computable blow up time\, location\, 
 and direction. The cusp-type solution at blow up is obtained by proving st
 ability of a  generic blowup profile in modulated self-similar variables. 
  The stability analysis controls the delicate interaction of wave families
  using pointwise bounds along Lagrangian trajectories\,  geometric vortici
 ty structure\, and high-order energy estimates in Sobolev spaces.\n
LOCATION:https://researchseminars.org/talk/IMS/45/
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