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


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 


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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