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Journal of Mathematical Fluid Mechanics

, Volume 13, Issue 2, pp 213–222 | Cite as

Non-Existence of Global Solutions For a Quasilinear Benney System

  • S. Antontsev
  • J. P. Dias
  • M. Figueira
  • F. Oliveira
Article

Abstract

Benney introduced in 1977 (cf. Stud Appl Math 56:81–94, 1977) a general strategy for deriving systems of nonlinear PDEs describing the interaction between long and short waves. In Dias et al. (CR Acad Sci Paris I 344:493–496, 2007) we have studied the local existence and unicity of solutions to a quasilinear version of these systems. In the present paper we prove that in some important cases global strong solutions do not exist.

Mathematics Subject Classification (2000)

35L70 35L65 76B15 

Keywords

Capillary/gravity waves mixed problem blow-up 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • S. Antontsev
    • 1
  • J. P. Dias
    • 1
  • M. Figueira
    • 1
  • F. Oliveira
    • 2
  1. 1.CMAF/UL and FCULLisbonPortugal
  2. 2.Centro de Matemática e Aplicações FCT-UNLMonte da CaparicaPortugal

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