2004 Prépublication d'Orsay numéro 2004-10 (01/03/2004)



KORTEWEG-DE VRIES AND BENJAMIN-ONO EQUATIONS ON ZHIDKOV SPACES.

GALLO, Clément - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex


Mots Clés : Korteweg-de Vries equation; Benjamin-Ono equation; Cauchy problem

Classification MSC : 35Q53; 35A07; 35A05.


Resumé :

Abstract :
Motivated by the study of the Cauchy problem with bore-like initial data, we show the ``well-posedness'' for Korteweg-de Vries and Benjamin-Ono equations with initial data in Zhidkov spaces Xs, with respectively s >1 and s >5/4. Here, ``well-posedness'' includes local (global in some cases) existence, uniqueness under a supplementary assumption and continuity with respect to the initial data.

Article : Fichier Dvi
Contact : Clement.Gallo@math.u-psud.fr