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

Alexander Kiselev; Vladimir Šverák

doi:10.4007/annals.2014.180.3.9

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

Alexander Kiselev, Vladimir Šverák

Mathematics

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121 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1205-1220
Number of pages	16
Journal	Annals of Mathematics
Volume	180
Issue number	3
DOIs	https://doi.org/10.4007/annals.2014.180.3.9
State	Published - Nov 2014

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

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