On the shallow water equations at low Reynolds number. (English) Zbl 0723.76033

A functional-analytic investigation of the shallow water equations for low Reynolds number, i.e. for the linearized form is presented. Existence of a solution is discussed for various formulations of the viscous term. A time implicit FEM is proposed and analyzed. In the appendix a rigorous derivation of the shallow water equation is presented.


76D33 Waves for incompressible viscous fluids
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A15 Variational methods applied to PDEs
35M20 PDE of composite type (MSC2000)
76D99 Incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics


Full Text: DOI


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