On the Slow Motion of Vortices in the Ginzburg–Landau Heat Flow
Jacob Rubinstein, Peter Sternberg · SIAM Journal on Mathematical Analysis · 1995
We study vortex motion in the Ginzburg–Landau flow. We consider this flow in the limit of large Ginzburg–Landau parameter. It is shown that when this parameter tends to infinity, the vortex mobility tends to zero. Our proof is based on an a priori estimate on the growth of a new weighted energy and on the recent work of Bethuel, Brezis, and Helein on $S^1 $-valued harmonic mappings in $R^2 $.