A shallow water approximation for water waves over a moving bottom

Fujiwara, Hiroyasu; Iguchi, Tatsuo

doi:10.2969/aspm/06410077

VOL. 64 | 2015 A shallow water approximation for water waves over a moving bottom

Hiroyasu Fujiwara, Tatsuo Iguchi

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

Adv. Stud. Pure Math., 2015: 77-88 (2015) DOI: 10.2969/aspm/06410077

Abstract

It is known that the Green–Naghdi equations are higher order approximations for the water wave problem in a shallow water regime. We derive corresponding equations in the case of moving bottom as a mode of tsunamis caused by the slow deformation of the bottom, and give a mathematically rigorous justification of the model.