Small scale creation for solutions of the incompressible two-dimensional Euler equation

Pages 1205-1220 from Volume 180 (2014), Issue 3 by Alexander Kiselev, Vladimir Šverák

Abstract

We construct an initial data for the two-dimensional Euler equation in a disk for which the gradient of vorticity exhibits double exponential growth in time for all times. This estimate is known to be sharp — the double exponential growth is the fastest possible growth rate.

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Keywords
, , , ,
DOI
https://doi.org/10.4007/annals.2014.180.3.9
MR
3245016
zbMATH
1304.35521
Milestones
Received: 1 November 2013
Revised: 7 April 2014
Accepted: 21 April 2014
Published online: 1 November 2014

Authors

Alexander Kiselev

Rice University, Houston, TX

Vladimir Šverák

University of Minnesota, Minneapolis, MN