Dynamics of incompressible vector fields

Applied Mathematics Letters

Volumn 12, Issue 4, 1999, Pages 39-42

  Ma, Tian ^a,b   Wang, S ^a  

^a INDIANA UNIVERSITY   (United States)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Divergence free vector fields; Fluid dynamics; Manifolds with boundary; Ocean atmosphere dynamics; Poincar Bendixson theorem; Poincar Hopf index theorem on manifolds with boundary; Structural classifications; Structural stability

Indexed keywords

EID: 0040312302     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(99)00030-0     Document Type: Article

References (10)

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3. H. Broer, Quasiperiodic flow near a codimension one singularity of a divergence free vector field in dimension three, In Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), Lecture Notes in Math, Volume 898, pp. 75-89, Springer, Berlin, (1981).
4. T. Ma and S. Wang, Structural classification and stability of divergence-free vector fields, (submitted).
5. T. Ma and S. Wang, Topological structure of divergence-free vector fields on 2-manifolds, (submitted).
6. H. Hopf, Abbildungsklassen n-dimensionaler mannigfaltigkeiten, Math. Annalen 96, 225-250, (1926).
7. J. Milnor, Topology from the Differentiable Viewpoint, based on notes by D.W. Weaver, Unversity Press of Virginia, Charlottesville, (1965).
8. T. Ma and S. Wang, Topological properties of vector fields and applications to fluid mechanics, (submitted).
9. J.L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of the atmosphere and applications, Nonlinearity 5, 237-288, (1992).
10. J.L. Lions, R. Temam and S. Wang, On the equations of large-scale ocean, Nonlinearity 5, 1007-1053, (1992).