A NEW FULLY JUSTIFIED ASYMPTOTIC MODEL FOR THE PROPAGATION OF INTERNAL WAVES IN THE CAMASSA-HOLM REGIME

作者：Duchene Vincent^*; Israwi Samer; Talhouk Raafat

来源：SIAM Journal on Mathematical Analysis, 2015, 47(1): 240-290.

DOI：10.1137/130947064

• internal waves
• asymptotic models
• Camassa-Holm regime

This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present a new Green-Naghdi type model in the Camassa-Holm (or medium amplitude) regime. This model is fully justified, in the sense that it is consistent and well-posed and that its solutions remain close to exact solutions of the full Euler system with corresponding initial data. Moreover, our system allows one to fully justify any well-posed and consistent lower order model, and, in particular, the so-called Constantin-Lannes approximation, which extends the classical Korteweg-de Vries model to the Camassa-Holm regime.

• 出版日期2015