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

• Autorzy: Cung The Anh
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35Q35: PDEs in connection with fluid mechanics
• 76B55: Internal waves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2009
• Tom: 96
• Numer: 2
• Strony: 127-161

Daty

wydano

2009

Twórcy

autor

Cung The Anh

• Department of Mathematics, Hanoi University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

Identyfikatory

DOI

10.4064/ap96-2-3