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Construction d’une base spéciale pour la résolution de quelques problèmes d’océanographie physique en dimension deux. (Construction of a special basis for the solution of some two dimensional problems in physical oceanography). (French) Zbl 0747.76047
Summary: This note deals with some peculiar properties of the eigenfunctions basis of the problem: \(-\Delta u=\lambda u\) in \(\Omega\subset\mathbb{R}^ 2\), with \(u\cdot n=0\) and \(\text{rot} u=0\) on the frontier \(\gamma\) of \(\Omega\), and where \(u\) is a function of \(\Omega\) into \(\mathbb{R}^ 2\). The main result pointed out is that a divergence free functions basis can be extracted, provinding a particulary suitable way of projecting the nonlinear terms of the equations presented.

76D33 Waves for incompressible viscous fluids
35Q30 Navier-Stokes equations
86A05 Hydrology, hydrography, oceanography