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arXiv · 1211.6780

Dynamics Of Ginzburg-Landau And Gross-Pitaevskii Vortices On Manifolds

Ko-Shin Chen·Peter Sternberg
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Abstract

We consider the dissipative heat flow and conservative Gross-Pitaevskii dynamics associated with the Ginzburg-Landau energy posed on a Riemannian 2-manifold M. We show the limiting vortices of the solutions to these two problems evolve according to the gradient flow and Hamiltonian point-vortex flow respectively, associated with the renormalized energy on M. For the heat flow, we then specialize to the case where M is a sphere and study the limiting system of ODE's and establish an annihilation result. Finally, for the Ginzburg-Landau heat flow on a sphere, we derive some weighted energy identities.

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Ko-Shin Chen, Peter Sternberg. 2012-11-28. Dynamics Of Ginzburg-Landau And Gross-Pitaevskii Vortices On Manifolds. https://doi.org/10.3934/dcds.2014.34.1905

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