In this paper, we consider some asymptotic models for internal waves in the small amplitude/small amplitude regime, which were derived recently by Bona, Lannes and Saut. We first prove that the Boussinesq/Full dispersion systems and the Boussinesq/Boussinesq systems can be derived from the Full dispersion/Full dispersion systems. Then using a contraction-mapping argument and the energy method, we will prove that the derived systems that are linearly well-posed are in fact locally nonlinearly well-posed in suitable Sobolev classes. In particular, we improve and extend some known results on the well-posedness of Boussinesq systems for surface waves. © 2009.

The Anh C.

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Từ khóa : Cauchy problem; Cauchy problems; Dispersion systems; Energy method; Internal waves; Wellposedness; Dispersions; Mapping; Shrinkage; Surface waves; Water waves; Dispersion (waves)