The main objective of this article is
to classify the structure of divergence-free vector fields
on general two-dimensional
compact manifold with or without boundaries.
First we prove a Limit Set Theorem, Theorem 2.1, a generalized version of the
Poincare-Bendixson to divergence-free vector fields on 2-manifolds
of nonzero genus. Namely, the $\omega$ (or $\alpha$) limit set of a regular
point of a regular divergence-free vector field is either a saddle point, or a
closed orbit, or a… Expand

The global structure of divergence-free vector fields on closed surfaces is investigated. We prove that if M is a closed surface and V is a divergence-free C-vector field with finitely many… Expand

We study in this article the large time
asymptotic structural stability and structural evolution in the
physical space for the solutions of the 2-D Navier-Stokes
equations with the periodic… Expand

We study in this article the structural bifurcation of divergence-free vector fields on a two-dimensional (2-D) com- pact manifold M. We prove that, for a one-parameter family of divergence-free… Expand

we see that ao is a group of homeomorphisms under the usual composition of maps. We define a to be the group of homeomorphisms generated by To01 and K where K(z) -+ 1/2. Then C/$o and C/$ are the… Expand