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.
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Communicated by H. Beirao da Veiga
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Antontsev, S., Dias, J.P., Figueira, M. et al. Non-Existence of Global Solutions For a Quasilinear Benney System. J. Math. Fluid Mech. 13, 213–222 (2011). https://doi.org/10.1007/s00021-009-0014-1