×

Global analysis of wavelet methods for Euler’s equation. (English) Zbl 1024.76007

Summary: Euler’s equation for the velocity \(u\) of an inviscid incompressible flow on Euclidean space admits the weak formulation \((\dot u,v)= ([u,v],u)\), 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.

MSC:

76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
65T60 Numerical methods for wavelets
Full Text: MNR