Global analysis of wavelet methods for Euler's equation

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.