Article

Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text
Advertising


Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    4 0 0 0


Comptes Rendus Mathématique
Volume 349, n° 19-20
pages 1063-1066 (novembre 2011)
Doi : 10.1016/j.crma.2011.09.009
Received : 15 July 2011 ;  accepted : 14 September 2011
Weak solutions to the incompressible Euler equations with vortex sheet initial data
Solutions faibles des équations dʼEuler incompressibles avec nappe de tourbillon comme donnée initiale
 

László Székelyhidi
Hausdorff Center for Mathematics, University of Bonn, Endenicher Allee 62, 53115 Bonn, Germany 

Abstract

We construct infinitely many admissible weak solutions to the incompressible Euler equations with initial data given by the classical vortex sheet. The construction is based on the method introduced recently in De Lellis and Székelyhidi Jr. (2009, 2010) [[2], [3]] using convex integration. In particular, the vorticity is not a bounded measure. Instead, the energy decreases in time due to a linearly expanding turbulent zone around the vortex sheet.

The full text of this article is available in PDF format.
Résumé

Nous construisons une infinité de solutions faibles admissibles des équations dʼEuler incompressibles avec nappes de tourbillons classiques pour données initiales. La construction repose sur la méthode introduite récemment dans De Lellis et Székelyhidi Jr. (2009, 2010) [[2], [3]] faisant appel à lʼintégration convexe. En particulier, la vorticité nʼest pas une mesure bornée. Au lieu de cela, lʼénergie décroît en temps, à cause dʼune zone turbulente, entourant la nappe de tourbillon et augmentant linéairement en temps.

The full text of this article is available in PDF format.


© 2011  Published by Elsevier Masson SAS de la part de Académie des sciences.
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Close
Article Outline
You can move this window by clicking on the headline
@@#110903@@