Derivation and well-posedness of Boussinesq/Boussinesq systems for internal waves

Volume 96 / 2009

Cung The Anh Annales Polonici Mathematici 96 (2009), 127-161 MSC: 76B55, 35Q35, 35A07. DOI: 10.4064/ap96-2-3


We consider the propagation of internal waves at the interface between two layers of immiscrible fluids of different densities, under the rigid lid assumption, with the presence of surface tension and with uneven bottoms. We are interested in the case where the flow has a Boussinesq structure in both the upper and lower fluid domains. Following the global strategy introduced recently by Bona, Lannes and Saut [J. Math. Pures Appl. 89 (2008)], we derive an asymptotic model in this regime, namely the Boussinesq/Boussinesq systems. Then using a contraction-mapping argument and energy methods, we prove that the derived systems which are linearly well-posed are in fact locally nonlinearly well-posed in suitable Sobolev classes. We recover and extend some known results on asymptotic models and well-posedness, for both surface waves and internal waves.


  • Cung The AnhDepartment of Mathematics
    Hanoi University of Education
    136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

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