Double exponential growth of the vorticity gradient for the two-dimensional Euler equation

Sergey A. Denisov

Type: Article

Publication Date: 2014-10-15

Citations: 67

DOI: https://doi.org/10.1090/s0002-9939-2014-12286-6

Abstract

For the two-dimensional Euler equation on the torus, we prove that the $L^\infty$–norm of the vorticity gradient can grow as double exponential over arbitrary long but finite time provided that at time zero it is already sufficiently large. The method is based on the perturbative analysis around the singular stationary solution studied by Bahouri and Chemin in 1994. Our result on the growth of the vorticity gradient is equivalent to the statement that the operator of Euler evolution is not bounded in the linear sense in Lipschitz norm for any time $t>0$.

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Proceedings of the American Mathematical Society - View
arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF

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+	Wandering solutions of Euler's D-2 equation	1991	Nikolai S. Nadirashvili
+	Equations de transport relatives � des champs de vecteurs non-lipschitziens et m�canique des fluides	1994	Hajer Bahouri J.-Y. Chemin
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