Double exponential growth of the vorticity gradient for the two-dimensional Euler equation
Analysis of PDEs
2012-05-07 v2 Mathematical Physics
math.MP
Abstract
For the two-dimensional Euler equation on the torus, we prove that the uniform norm of the vorticity gradient can grow as double exponential over arbitrarily long but finite time provided that at time zero it is already sufficiently large. Our result is equivalent to the statement that the Euler evolutions is linearly unbounded in Lipschitz norm for any time t>0.
Cite
@article{arxiv.1201.1771,
title = {Double exponential growth of the vorticity gradient for the two-dimensional Euler equation},
author = {Sergey A. Denisov},
journal= {arXiv preprint arXiv:1201.1771},
year = {2012}
}
Comments
References added, typos fixed, the reinterpretation of the main statement is given