| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
[2] Univ Fed Sergipe, Ctr Cincias Exatas & Tecnol, Sao Cristovao - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF NONLINEAR SCIENCE; v. 27, n. 5, p. 1609-1640, OCT 2017. |
| Web of Science Citations: | 3 |
| Abstract | |
The equations of motion for a system of point vortices on an oriented Riemannian surface of finite topological type are presented. The equations are obtained from a Green's function on the surface. The uniqueness of the Green's function is established under hydrodynamic conditions at the surface's boundaries and ends. The hydrodynamic force on a point vortex is computed using a new weak formulation of Euler's equation adapted to the point vortex context. An analogy between the hydrodynamic force on a massive point vortex and the electromagnetic force on a massive electric charge is presented as well as the equations of motion for massive vortices. Any noncompact Riemann surface admits a unique Riemannian metric such that a single vortex in the surface does not move ({''}Steady Vortex Metric{''}). Some examples of surfaces with steady vortex metric isometrically embedded in R-3 are presented. (AU) | |
| FAPESP's process: | 11/16265-8 - Low dimensional dynamics |
| Grantee: | Edson Vargas |
| Support Opportunities: | Research Projects - Thematic Grants |