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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Regularizing effect of the forward energy cascade in the inviscid dyadic model
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by Alexey Cheskidov and Karen Zaya PDF
Proc. Amer. Math. Soc. 144 (2016), 73-85 Request permission

Abstract:

We study the inviscid dyadic model of the Euler equations and prove some regularizing properties of the nonlinear term that occur due to forward energy cascade. We show every solution must have $\frac {3}{5}$ $L^2$-based (or $\frac {1}{10}$ $L^3$-based) regularity for all positive time. We conjecture this holds up to Onsager’s scaling, where the $L^2$-based exponent is $\frac {5}{6}$ and the $L^3$-based exponent is $\frac {1}{3}$.
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Additional Information
  • Alexey Cheskidov
  • Affiliation: Department of Mathematics, Statistics, and Mathematical Computer Science, University of Illinois at Chicago, 851 South Morgan Street (M/C 249), Chicago, Illinois 60607
  • MR Author ID: 680409
  • ORCID: 0000-0002-2589-2047
  • Email: acheskid@uic.edu
  • Karen Zaya
  • Affiliation: Department of Mathematics, Statistics, and Mathematical Computer Science, University of Illinois at Chicago, 851 South Morgan Street (M/C 249), Chicago, Illinois 60607
  • Email: kzaya2@uic.edu
  • Received by editor(s): October 28, 2013
  • Received by editor(s) in revised form: November 13, 2013, February 3, 2014, February 6, 2014, and February 28, 2014
  • Published electronically: September 11, 2015
  • Communicated by: Joachim Krieger
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 73-85
  • MSC (2010): Primary 35Q31, 76B03
  • DOI: https://doi.org/10.1090/proc/12494
  • MathSciNet review: 3415578