Comptes Rendus
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

João-Paulo Dias1 ; Mário Figueira1 ; Filipe Oliveira2
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, Volume 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
João-Paulo Dias 1 ; Mário Figueira 1 ; Filipe Oliveira 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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     title = {Existence of local strong solutions for a quasilinear {Benney} system},
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João-Paulo Dias; Mário Figueira; Filipe Oliveira. Existence of local strong solutions for a quasilinear Benney system. Comptes Rendus. Mathématique, Volume 344 (2007) no. 8, pp. 493-496. doi : 10.1016/j.crma.2007.03.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.005/

[1] D.J. Benney A general theory for interactions between short and long waves, Stud. Appl. Math., Volume 56 (1977), pp. 81-94

[2] J.P. Dias, M. Figueira, Existence of weak solutions for a quasilinear version of Benney equations, J. Hyperbolic Differential Equations, in press

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

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

[5] Y. Shibata; Y. Tsutsumi Local existence of solutions for the initial boundary problem of fully nonlinear wave equation, Nonlinear Anal. TMA, Volume 11 (1987), pp. 335-365

[6] M. Tsutsumi; S. Hatano Well-posedness of the Cauchy problem for the long wave–short wave resonance equations, Nonlinear Anal. TMA, Volume 22 (1994), pp. 155-171

[7] M. Tsutsumi; S. Hatano 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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