Small scale creation of the Lagrangian flow in 2d perfect fluids
Ayman Rimah Said, Cambridge University
In this talk I will present a recent result showing that for all solutions of the 2d Euler equations with initial vorticity with finite Sobolev smoothness then an initial data dependent norm of the associated Lagrangian flow blows up in infinite 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 solution. 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 quantitative phenomenon behind a microlocal generalised Lyapunov function constructed by Shnirelman.
** IAC-CNR, via dei Taurini 19 -- aula I piano **
Data inizio
