Uniqueness of strong solution for a 1D viscous bi-layer Shallow Water model

Abstract

The aim of this paper is to prove the uniqueness of strong solutionof a one dimensional viscous bilayer shallow water model. Our analy-sis is based on some new useful estimate namely BD entropy and on amethod developed by Mellet and Vasseur in [14] to prove the existenceand uniqueness on some compressible one dimensional Navier-Stokessystem. Under suitable assumptions on the solutions and using Gron-wall Lemma, we obtain the uniqueness of strong solution. We performour analysis in periodic domain with periodic boundaries conditions.