Study of the non-viscous equatorial shallow water system

The aim of this article is to prove the convergence of solutions of penalized systems describing given by equatorial shallow water equations without viscosity towards the solution of the limit system, generalizing the results of A. Dutrifoy, A. Majda and S. Schochet (2009) in [3] to all initial data even ill-prepared. A similar result is proved by I. Gallagher and L. Saint-Raymond (2006) in [4] but with a viscous fluid. We will also give a necessary and sufficient condition for a global existence of the solution of the limit system proving that the Kelvin waves lead to an explosion in finite time as a Burger equation. (C) 2012 Elsevier Masson SAS. All rights reserved.