D S ] 2 5 Se p 20 01 Point vortices on the sphere : a case with opposite vorticities

@inproceedings{LaurentPolz2002DS,
  title={D S ] 2 5 Se p 20 01 Point vortices on the sphere : a case with opposite vorticities},
  author={F Laurent-Polz},
  year={2002}
}
  • F Laurent-Polz
  • Published 2002
We study systems formed of 2N point vortices on a sphere with N vortices of strength +1 and N vortices of strength −1. In this case, the Hamil-tonian is conserved by the symmetry which exchanges the positive vortices with the negative vortices. We prove the existence of some fixed and relative equilib-ria, and then study their stability with the " Energy Momentum Method ". Most of the results obtained are nonlinear stability results. To end, some bifurcations are described. 

References

Publications referenced by this paper.
Showing 1-5 of 5 references

Stability of Hamiltonian relative equilibria Principle of symmetric criticality

  • T. Ratiu Ortega
  • Comm . Math . Phys .
  • 1979

Motion of three point vortices on a sphere Collapse of three vortices on a sphere Rotating ngon / kn - gon vortex configurations

  • J. Montaldi Lim, M. Roberts
  • J . Nonlinear Sci .

The equilibrium and stability of a row of point vortices Asymmetric equilibrium patterns of point vortices

  • I. Stewart, D. Schaeffer

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