A theorem of uniqueness for an inviscid dyadic model

Barbato, D.; Flandoli, Franco; Morandin, Francesco

doi:10.1016/j.crma.2010.03.007

Ordinary Differential Equations

A theorem of uniqueness for an inviscid dyadic model
[Un théorème d'unicité pour un modèle dyadique non visqueux]

Présenté par : Jean-Michel Bony

Barbato, D.¹ ; Flandoli, Franco ² ; Morandin, Francesco ³

¹ Dipartimento di Matematica Pura e Applicata, Università di Padova, via Trieste, 63, 35121 Padova, Italy
² Dipartimento di Matematica Applicata, Università di Pisa, via Buonarroti, 1, 56127 Pisa, Italy
³ Dipartimento di Matematica, Università di Parma, viale G.P. Usberti, 53A, 43124 Parma, Italy

Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 525-528.

Résumé
Abstract

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 $K$ assez large, ce qui implique en particulier l'existence et l'unicité dans $l^{2}$ pour toute condition initiale positive dans $l^{2}$ .

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 $K$ that implies in particular global existence and uniqueness in $l^{2}$ for all initial positive conditions in $l^{2}$ .

Reçu le : 2009-10-25
Accepté le : 2010-03-09
Publié le : 2010-03-29

DOI : 10.1016/j.crma.2010.03.007

Affiliations des auteurs :

Barbato, D. ¹ ; Flandoli, Franco ² ; Morandin, Francesco ³

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Barbato, D.; Flandoli, Franco; Morandin, Francesco. A theorem of uniqueness for an inviscid dyadic model. Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 525-528. doi : 10.1016/j.crma.2010.03.007. http://www.numdam.org/articles/10.1016/j.crma.2010.03.007/

Bibliographie
Cité par

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