Global analysis of wavelet methods for Euler's equation

W. Lawton

Matematičeskoe modelirovanie, Tome 14 (2002) no. 5, pp. 75-88.

Résumé

Euler's equation for the velocity и of an inviscid incompressible flow on Euclidean space admits the weak formulation $(\dot u,v)=([u,v],w)$, for all divergence free vector fields $v$. Here $(\,\cdot\,,\,\cdot\,)$ denotes the scalar product that represents kinetic energy and $[\,\cdot\,,\,\cdot\,]$ denotes the Poisson bracket. We employ global analysis methods based on this formulation to discuss Faedo–Galerkin approximation using divergence free wavelets.

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