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SUMMARY:Small scale creation of the Lagrangian flow in 2d perfect fluids
DTSTART:20240412T141500
DTSTAMP:20260506T233101Z
UID:59f8f981076b26c71f3ececd053e7bc859d264098dfff1c1cfc451c9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Ayman Said (Cambridge Univ.)\nAbstract: In this talk I wil
 l present a recent result showing that for all solutions of the 2d Euler e
 quations with initial vorticity with finite Sobolev smoothness then an ini
 tial data dependent norm  of the associated Lagrangian flow blows up in i
 nfinite time at least like $t^{\\frac{1}{3}}$. This initial data dependent
  norm quantifies the exact $L^2$ decay of the Fourier transform of the sol
 ution. This adapted norm turns out to be the exact quantity that controls 
 a low to high frequency cascade whichI I will then show to be the quantita
 tive phenomenon behind a microlocal generalised Lyapunov function construc
 ted by Shnirelman.\n 
LOCATION:MA B1 11 https://plan.epfl.ch/?room==MA%20B1%2011
STATUS:CONFIRMED
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