Geodesic
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, Franco2 ; Morandin, Francesco3
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.

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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.

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.

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

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 
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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://geodesic.mathdoc.fr/articles/10.1016/j.crma.2010.03.007/

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

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

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

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