Weak solutions of one-dimensional pollutant transport model

Abstract

We consider a one-dimensional bilayer model coupling shallow water and Reynolds
lubrication equations that is a similar model to [European J. Applied Mathematics 24(6) (2013), 803-833]. The model considered is represented by the two superposed immiscible uids. Under a physical hypothesis, we show the existence of global weak solution in time in periodic domain with periodic boundaries conditions.