Asymptotic solutions of Navier-Stokes equations and topological invariants of vector fields and Liouville foliations

We construct asymptotic solutions of the Navier-Stokes equations. Such solutions describe periodic systems of localized vortices and are related to topological invariants of divergence-free vector fields on two-dimensional cylinders or tori and to the Fomenko invariants of Liouville foliations. The equations describing the evolution of a vortex system are given on a graph that is a set of trajectories of the divergence-free field or a set of Liouville tori.