Comptes Rendus
no. 9-10
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. Barbato1 ; Franco Flandoli2 ; Francesco Morandin3
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.

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 l2 pour toute condition initiale positive dans l2.

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 l2 for all initial positive conditions in l2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.03.007

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 
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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/

[1] D. Barbato; F. Flandoli; F. Morandin Energy dissipation and self-similar solutions for an unforced inviscid dyadic model (Trans. Amer. Math. Soc., in press) | arXiv

[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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