No local double exponential gradient growth in hyperbolic flow for the 2d Euler equation
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- by Vu Hoang and Maria Radosz PDF
- Trans. Amer. Math. Soc. 369 (2017), 7169-7211 Request permission
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.References
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Additional Information
- Vu Hoang
- Affiliation: Department of Mathematics-MS 136, Rice University, Box 1892, Houston, Texas 77251-1892
- MR Author ID: 893316
- 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
- MR Author ID: 1065732
- Email: maria_radosz@hotmail.com
- Received by editor(s): July 9, 2015
- Received by editor(s) in revised form: December 30, 2015
- Published electronically: February 13, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 7169-7211
- MSC (2010): Primary 35Q35, 35Q31; Secondary 76B99
- DOI: https://doi.org/10.1090/tran/6900
- MathSciNet review: 3683107