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SUMMARY:Philip Isett (University of Texas at Austin)
DTSTART:20200709T150000Z
DTEND:20200709T155000Z
DTSTAMP:20260423T021119Z
UID:IMS/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/39/">A P
 roof of Onsager’s Conjecture for the Incompressible Euler Equations</a>\
 nby Philip Isett (University of Texas at Austin) as part of PDE seminar vi
 a Zoom\n\n\nAbstract\nIn an effort to explain how anomalous dissipation of
  energy occurs in hydrodynamic turbulence\, Onsager conjectured in 1949 th
 at weak solutions to the incompressible Euler equations may fail to exhibi
 t conservation of energy if their spatial regularity is below 1/3-Hölder.
   I will discuss a proof of this conjecture that shows that there are nonz
 ero\, (1/3-\\epsilon)-Hölder Euler flows in 3D that have compact support 
 in time.  The construction is based on a method known as "convex integrati
 on\," which has its origins in the work of Nash on isometric embeddings wi
 th low codimension and low regularity.  A version of this method was first
  developed for the incompressible Euler equations by De Lellis and Székel
 yhidi to build Hölder-continuous Euler flows that fail to conserve energy
 \, and was later improved by Isett and by Buckmaster-De Lellis-Székelyhid
 i to obtain further partial results towards Onsager's conjecture.  The pro
 of of the full conjecture combines convex integration using the “Mikado 
 flows” introduced by Daneri-Székelyhidi with a new “gluing approximat
 ion” technique.The latter technique exploits a special structure in the 
 linearization of the incompressible Euler equations.\n\nPlease visit the f
 ollowing link: https://nguyenquochung1241.wixsite.com/qhung/post/pde-semin
 ar-via-zoom to get more information.\n
LOCATION:https://researchseminars.org/talk/IMS/39/
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