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

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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Authors

Alexander Kiselev

Rice University, Houston, TX

Vladimir Šverák

University of Minnesota, Minneapolis, MN