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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 525-528 (mai 2010)
Doi : 10.1016/j.crma.2010.03.007
Received : 25 October 2009 ;  accepted : 9 Mars 2010
A theorem of uniqueness for an inviscid dyadic model
Un théorème d’unicité pour un modèle dyadique non visqueux
 

D. Barbato a , Franco Flandoli b , Francesco Morandin c
a Dipartimento di Matematica Pura e Applicata, Università di Padova, via Trieste, 63, 35121 Padova, Italy 
b Dipartimento di Matematica Applicata, Università di Pisa, via Buonarroti, 1, 56127 Pisa, Italy 
c Dipartimento di Matematica, Università di Parma, viale G.P. Usberti, 53A, 43124 Parma, Italy 

Abstract

We consider the solutions of the Cauchy problem for a dyadic model of Euler equations. We prove global existence and uniqueness of Leray–Hopf solutions in a rather large class   that implies in particular global existence and uniqueness in   for all initial positive conditions in  .

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Résumé

Nous considérons les solutions du problème de Cauchy pour un modèle dyadique d’équations d’Euler. Nous démontrons l’existence et l’unicité globales des solutions de Leray–Hopf dans une classe   assez large, ce qui implique en particulier l’existence et l’unicité dans   pour toute condition initiale positive dans  .

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


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