# zbMATH — the first resource for mathematics

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.

##### MSC:
 76D33 Waves for incompressible viscous fluids 35Q30 Navier-Stokes equations 86A05 Hydrology, hydrography, oceanography
##### Keywords:
eigenfunctions basis; divergence free functions basis