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On admissibility criteria for weak solutions of the Euler equations


De Lellis, C; Székelyhidi, L (2010). On admissibility criteria for weak solutions of the Euler equations. Archiv for Rational Mechanics and Analysis, 195(1):225-260.

Abstract

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper, we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct, in more than one space dimension, we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique.

Abstract

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper, we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct, in more than one space dimension, we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Mathematics (miscellaneous)
Physical Sciences > Mechanical Engineering
Language:English
Date:2010
Deposited On:23 Dec 2010 16:06
Last Modified:28 Jun 2022 11:36
Publisher:Springer
ISSN:0003-9527
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00205-008-0201-x
Related URLs:http://arxiv.org/abs/0712.3288
  • Content: Accepted Version
  • Description: Accepted manuscript, Version 3?
  • Content: Accepted Version
  • Description: Accepted manuscript, Version 2
  • Content: Accepted Version
  • Description: Accepted manuscript, Version 1
  • Content: Published Version
  • Language: English
  • Description: Nationallizenz 142-005