# Comparison of solutions of Boussinesq systems

* Corresponding author 1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée 2 COFFEE - COmplex Flows For Energy and Environment CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351 3 JAD - Laboratoire Jean Alexandre Dieudonné

Abstract : We compare the solution of the generalized Boussinesq systems, for various values of a,b,c,d, \begin{eqnarray} onumber \eta t +u x +\varepsilon \eta u x +au {xxx}-b\eta {xxt} &=& 0 \\ onumber u t +\eta x +\varepsilon uu x +c\eta {xxx} -du {xxt} &=&0.\end{eqnarray}These systems describe the two-way propagation of small amplitude long waves in shallow water. We prove, using an energy method introduced by Bona, Pritchard and Scott, that respective solutions of Boussinesq systems, starting from the same initial datum, remain close on a time interval inversely proportional to the wave amplitude.

Keywords : Boussinesq systems Comparison Energy method

Author: Youcef Mammeri - Yumeng Zhang -

Source: https://hal.archives-ouvertes.fr/