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Well-posedness of the cauchy problem for models of large amplitude internal waves

Guyenne, Philippe ; Lannes, David ; Saut, Jean-Claude

Nonlinearity, 2010, Vol.23(2), pp.237-275 [Periódico revisado por pares]

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  • Título:
    Well-posedness of the cauchy problem for models of large amplitude internal waves
  • Autor: Guyenne, Philippe ; Lannes, David ; Saut, Jean-Claude
  • Assuntos: Mathematical Models ; Computational Fluid Dynamics ; Cauchy Problem ; Fluid Flow ; Fluids ; Density ; Amplitudes ; Asymptotic Properties ; Internal Waves ; Computer Simulation ; Constrictions ; Shock Waves ; Solid State Milieux (General) (So) ; Article
  • É parte de: Nonlinearity, 2010, Vol.23(2), pp.237-275
  • Descrição: We consider in this paper the shallow-water/shallow-water asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 136), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 53866) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of hyperbolic type and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves.
  • Idioma: Inglês

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