GLOBAL STRUCTURE OF 2-D INCOMPRESSIBLE FLOWS

@article{Ma2001GLOBALSO,
  title={GLOBAL STRUCTURE OF 2-D INCOMPRESSIBLE FLOWS},
  author={Tian Ma and Shouhong Wang},
  journal={Discrete and Continuous Dynamical Systems},
  year={2001},
  volume={7},
  pages={431-445}
}
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… 

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