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