On the Existence of Global Weak Solutions to 1D Pollutant Transport Model

Brahima Roamba, Jean de Dieu ZABSONRE and Yacouba Zongo

Journal of Mathematics Research, 2017, vol. 9, issue 4, 124-134

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, Zabsonr\'{e}\& Zongo, 2017). The model considered is represented by the two superposed immiscible fluids. A similar model was studied in (Zabsonr\'{e} Lucas \& Fernandez-Nieto, 2009) but the authors do not take into account the intermolecular forces. Without hypothesis about the unknowns as in (Roamba, Zabsonr\'{e}\& Zongo, 2017), we show the existence of global weak solution in time in a periodic domain.

Keywords: shallow water equations; bilayer models; viscosity; friction; capillarity; intermolecular forces (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:124-134

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