Geodesic
On some Boussinesq systems in two space dimensions : theory and numerical analysis
Dougalis, Vassilios A. ; Mitsotakis, Dimitrios E.  ; Saut, Jean-Claude1 
1 UMR de Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405 Orsay, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 5, pp. 825-854

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A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized by Galerkin-finite element methods, and error estimates are proved for the resulting continuous time semidiscretizations. Results of numerical experiments are also presented with the aim of studying properties of line solitary waves and expanding wave solutions of these systems.

DOI : 10.1051/m2an:2007043
Classification : 35Q53, 65M60, 76B15
Keywords: Boussinesq systems in two space dimensions, water wave theory, nonlinear dispersive wave equations, Galerkin-finite element methods for Boussinesq systems

Dougalis, Vassilios A.  ; Mitsotakis, Dimitrios E.  ; Saut, Jean-Claude 1

1 UMR de Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405 Orsay, France. 
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     title = {On some {Boussinesq} systems in two space dimensions : theory and numerical analysis},
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Dougalis, Vassilios A.; Mitsotakis, Dimitrios E.; Saut, Jean-Claude. On some Boussinesq systems in two space dimensions : theory and numerical analysis. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 5, pp. 825-854. doi: 10.1051/m2an:2007043

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