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
    6 0 0 0


Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 885-890 (août 2010)
Doi : 10.1016/j.crma.2010.06.025
Received : 4 January 2010 ;  accepted : 29 June 2010
  and   regularity of the solution of a steady transport equation
Régularité dans   et   de la solution d'une équation de transport stationnaire
 

Vivette Girault a, b , Luc Tartar c
a UPMC–Paris 6, CNRS, UMR 7598, 75005 Paris, France 
b Department of Mathematics, TAMU, College Station, TX 77843, USA 
c Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA 

Abstract

We consider a steady transport system of equations in a bounded Lipschitz domain of  ,  , with a divergence-free transport velocity in  , tangential on the boundary. By means of two regularizations, first with a viscous penalty term and next with a Yosida approximation, we prove that an   data,  , yields a solution in  . We apply this result to establish that for data in   and transport velocity in  , sufficiently small, the solution of a scalar transport equation belongs to  .

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

On considère une équation de transport vectorielle stationnaire dans un domaine Lipschitz borné de  ,  , avec une vitesse de transport dans  , à divergence nulle, tangentielle sur le bord. A l'aide de deux régularisations, d'abord avec un terme visqueux de pénalisation et ensuite avec une approximation de Yosida, on montre que si la donnée est dans  ,  , alors la solution est dans  . On applique ce résultat pour démontrer que si la donnée d'une équation de transport scalaire est dans   et la vitesse de transport est dans  , assez petite, alors la solution est dans  .

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


© 2010  Académie des sciences@@#104156@@
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@@