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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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On the radius of analyticity of solutions to the three-dimensional Euler equations
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by Igor Kukavica and Vlad Vicol PDF
Proc. Amer. Math. Soc. 137 (2009), 669-677 Request permission

Abstract:

We address the problem of analyticity of smooth solutions $u$ of the incompressible Euler equations. If the initial datum is real–analytic, the solution remains real–analytic as long as $\int _{0}^{t} \left \Vert {\nabla u(\cdot ,s)}\right \Vert _{L^\infty } ds< \infty$. Using a Gevrey-class approach we obtain lower bounds on the radius of space analyticity which depend algebraically on $\exp {\int _{0}^{t} \left \Vert {\nabla u(\cdot ,s)}\right \Vert _{L^\infty }}ds$. In particular, we answer in the positive a question posed by Levermore and Oliver.
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Additional Information
  • Igor Kukavica
  • Affiliation: Department of Mathematics, University of Southern California, 3620 S. Vermont Avenue, Los Angeles, California 90089
  • MR Author ID: 314775
  • Email: kukavica@usc.edu
  • Vlad Vicol
  • Affiliation: Department of Mathematics, University of Southern California, 3620 S. Vermont Avenue, Los Angeles, California 90089
  • MR Author ID: 846012
  • ORCID: setImmediate$0.00243841196800898$2
  • Email: vicol@usc.edu
  • Received by editor(s): November 13, 2007
  • Published electronically: September 16, 2008
  • Additional Notes: Both authors were supported in part by the NSF grant DMS-0604886.
  • Communicated by: Matthew J. Gursky
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 669-677
  • MSC (2000): Primary 76B03, 35L60
  • DOI: https://doi.org/10.1090/S0002-9939-08-09693-7
  • MathSciNet review: 2448589