no. 8
Partial Differential Equations
Existence of local strong solutions for a quasilinear Benney system
[Existence d'une solution locale forte pour un système de Benney quasilinéaire]

Présenté par : Gilles Lebeau

Dias, João-Paulo1 ; Figueira, Mário1 ; Oliveira, Filipe2
1 CMAF/UL and FCUL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
2 Dep. Matemática, FCT/UNL, Monte da Caparica, Portugal
Comptes Rendus. Mathématique, Tome 344 (2007) no. 8, pp. 493-496.

Nous prouvons dans cette Note l'existence et unicité d'une solution locale forte du problème de Cauchy pour le système de Benney quasilinéaire.

We prove in this Note the existence and uniqueness of a strong local solution to the Cauchy problem for the quasilinear Benney system.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.03.005
Dias, João-Paulo 1 ; Figueira, Mário 1 ; Oliveira, Filipe 2

1 CMAF/UL and FCUL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
2 Dep. Matemática, FCT/UNL, Monte da Caparica, Portugal 
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Dias, João-Paulo; Figueira, Mário; Oliveira, Filipe. Existence of local strong solutions for a quasilinear Benney system. Comptes Rendus. Mathématique, Tome 344 (2007) no. 8, pp. 493-496. doi : 10.1016/j.crma.2007.03.005. http://www.numdam.org/articles/10.1016/j.crma.2007.03.005/

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[3] Kato, T. Quasi-linear equations of evolution, with applications to partial differential equations, Lecture Notes in Math., vol. 448, Springer, 1975, pp. 25-70

[4] Oliveira, F. Stability of the solitons for the one-dimensional Zakharov–Rubenchik equation, Physica D, Volume 175 (2003), pp. 220-240

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[7] Tsutsumi, M.; Hatano, S. Well-posedness of the Cauchy problem for Benney's first equations of long wave short wave interactions, Funkcial. Ekvac., Volume 37 (1994), pp. 289-316

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