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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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