Abstract :

We show that the vorticity of a viscous flow in R^3 admits an atomic decomposition of the form \omega(x,t)=\sum_{k=1}^\infty \omega_k(x-x_k,t), with localized and oscillating building blocks \omega_k, if such a property is satisfied at the beginning of the evolution. We also study the long time behavior of an isolated coherent structure and the special behavior of flows with highly oscillating vorticities.