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No local double exponential gradient growth in hyperbolic flow for the 2d Euler equation


Authors: Vu Hoang and Maria Radosz
Journal: Trans. Amer. Math. Soc. 369 (2017), 7169-7211
MSC (2010): Primary 35Q35, 35Q31; Secondary 76B99
DOI: https://doi.org/10.1090/tran/6900
Published electronically: February 13, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider smooth, double-odd solutions of the two-dimensional Euler equation in $ [-1, 1)^2$ with periodic boundary conditions. This situation is a possible candidate to exhibit strong gradient growth near the origin. We analyze the flow in a small box around the origin in a strongly hyperbolic regime and prove that the compression of the fluid induced by the hyperbolic flow alone is not sufficient to create double-exponential growth of the gradient.


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Additional Information

Vu Hoang
Affiliation: Department of Mathematics-MS 136, Rice University, Box 1892, Houston, Texas 77251-1892
Email: vu.hoang@rice.edu

Maria Radosz
Affiliation: Department of Mathematics-MS 136, Rice University, Box 1892, Houston, Texas 77251-1892 – and – Institute for Analysis, Karlsruhe Institute for Technology (KIT), Kaiserstrasse 89, 76133 Karlsruhe, Germany
Email: maria_radosz@hotmail.com

DOI: https://doi.org/10.1090/tran/6900
Received by editor(s): July 9, 2015
Received by editor(s) in revised form: December 30, 2015
Published electronically: February 13, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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