IUMJ

Title: Quantitative Equipartition of the Ginzburg-Landau Energy with Applications

Authors: Daniel Spirn and Matthias Kurzke

Issue: Volume 59 (2010), Issue 6, 2077-2092

Abstract:

We study the Ginzburg-Landau energy of a single vortex and prove a quantitative estimate for the anisotropy of the stress-energy tensor. In particular we establish an asymptotic rate of equipartitioning of the energy along each direction. By means of an explicit example, this rate is shown to be optimal up to a constant. The result has applications in the study of the nonlinear wave equation and Ginzburg-Landau heat flow.