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Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 499-503 (mai 2012)
Doi : 10.1016/j.crma.2012.05.007
Received : 18 November 2011 ;  accepted : 16 May 2012
A Note on the Cauchy problem for the 2D generalized Zakharov–Kuznetsov equations
Une Note sur le problème de Cauchy pour les équations de Zakharov–Kuznetsov 2D généralisées
 

Francis Ribaud a , Stéphane Vento b
a Laboratoire dʼanalyse et de mathématiques appliquées, Université Paris-est, 5 boulevard Descartes, Champs-Sur-Marne, 77454 Marne-La-Vallée cedex 2, France 
b Laboratoire analyse, géométrie et applications, Université Paris 13, Institut Galilée, 99, avenue J.B. Clément, 93430 Villetaneuse, France 

Abstract

In this Note we study the generalized 2D Zakharov–Kuznetsov equations   for  . By an iterative method we prove the local well-posedness of these equations in the Sobolev spaces   for   if  ,   if   and   if  .

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

Nous étudions dans cette Note les équations de Zakharov–Kuznetsov 2D généralisées   pour  . Il est établi que le problème de Cauchy peut être résolu par une méthode itérative dans les espaces de Sobolev   pour   si  ,   si   et   si  .

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


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