Abstract

We consider a one-dimensionnal bilayer model coupling shallow water and Reynolds lubrication equations with a molecular interactions between molecules. These molecular interactions give rise to intermolecular forces, namely the long-range van der Waals forces and short-range Born intermolecular forces. In this paper, an expression will be used to take into account all these intermolecular forces. Our model is a similar model studied in (Roamba, Zabsonré & Zongo, 2017). The model considered is represented by the two superposed immiscible fluids. A similar model was studied in (Zabsonré Lucas & Fernandez-Nieto, 2009) but the authors do not take into  account the intermolecular forces. Without hypothesis about the unknowns as in (Roamba, Zabsonré & Zongo, 2017), we show the existence of global weak solution in time in a periodic domain.

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