Structural descriptions of limits of the parabolic Ginzburg-Landau equation on closed manifolds

Andrew Colinet

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arXiv · 2107.13582

Structural descriptions of limits of the parabolic Ginzburg-Landau equation on closed manifolds

Andrew Colinet

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Abstract

In the setting of a compact Riemannian manifold of dimension $N\ge3$ we provide a structural description of the limiting behaviour of the energy measures of solutions to the parabolic Ginzburg-Landau equation. In particular, we provide a decomposition of the limiting energy measure into a diffuse part, which is absolutely continuous with respect to the volume measure, and a concentrated part supported on a codimension $2$ rectifiable subset. We also demonstrate that the time evolution of the diffuse part is determined by the heat equation while the concentrated part evolves according to a Brakke flow. This paper extends the work of Bethuel, Orlandi, and Smets.

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Andrew Colinet. 2021-07-28. Structural descriptions of limits of the parabolic Ginzburg-Landau equation on closed manifolds. https://arxiv.org/abs/2107.13582

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