A theorem of uniqueness for an inviscid dyadic model

D. Barbato; Franco Flandoli; Francesco Morandin

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

D. Barbato ¹ ; Franco Flandoli ² ; Francesco Morandin 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, Volume 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 :

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

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D. Barbato; Franco Flandoli; Francesco Morandin. A theorem of uniqueness for an inviscid dyadic model. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 525-528. doi : 10.1016/j.crma.2010.03.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.007/

Bibliographie
Cité par

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[2] D. Barbato; F. Flandoli; F. Morandin Uniqueness for a stochastic inviscid dyadic model (Proc. Amer. Math. Soc., in press) | arXiv

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[4] C. De Lellis; L. Székelyhidi On admissibility criteria for weak solutions of the Euler equations | arXiv

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[9] F. Waleffe On some dyadic models of the Euler equations, Proc. Amer. Math. Soc., Volume 134 (2006), pp. 2913-2922

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