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.