From Navier–Stokes equations to shallow waters with viscosity by asymptotic analysis

Article type: Research Article

Authors: Rodríguez, José M.^; | Taboada-Vázquez, Raquel

Affiliations: Departamento de Métodos Matemáticos y de Representación, E.T.S. de Arquitectura, Universidade da Coruña, Campus da Zapateira, s/n. 15071 A Coruña, Spain E-mail: [email protected] | Departamento de Métodos Matemáticos y de Representación, E.S. Mariña Civil, Universidade da Coruña, Paseo de Ronda, 15011 A Coruña, Spain E-mail: [email protected]

Note: [] Corresponding author.

Abstract: In this paper, we study the Navier–Stokes equations in a domain with small depth. With this aim, we introduce a small adimensional parameter ε related to the depth. First we make a change of variable to a domain independent of ε and then we use asymptotic analysis to study what happens when ε becomes small. In this way we obtain a model for ε small that, after coming back to the original domain and without making a priori assumptions about velocity or pressure behavior, gives us a shallow water model including a new diffusion term.

Keywords: asymptotic analysis, shallow waters with viscosity

Journal: Asymptotic Analysis, vol. 43, no. 4, pp. 267-285, 2005