Existence of local strong solutions for a quasilinear Benney system

João-Paulo Dias; Mário Figueira; Filipe Oliveira

doi:10.1016/j.crma.2007.03.005

Partial Differential Equations

Existence of local strong solutions for a quasilinear Benney system

Presented by: Gilles Lebeau

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

Comptes Rendus. Mathématique, Volume 344 (2007) no. 8, pp. 493-496.

Abstract (Original language)
Résumé

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

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

Received: 2007-01-03
Accepted: 2007-03-06
Published online: 2007-04-15

DOI: 10.1016/j.crma.2007.03.005

Author's affiliations:

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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     author = {Jo\~ao-Paulo Dias and M\'ario Figueira and Filipe Oliveira},
     title = {Existence of local strong solutions for a quasilinear {Benney} system},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {493--496},
     publisher = {Elsevier},
     volume = {344},
     number = {8},
     year = {2007},
     doi = {10.1016/j.crma.2007.03.005},
     language = {en},
}

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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/

References
Cited by

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[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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