Limiting Motion for the Parabolic Ginzburg-Landau Equation with Infinite Energy Data

作者：Cote Delphine; Cote Raphael^*

来源：Communications in Mathematical Physics, 2017, 350(2): 507-568.

DOI：10.1007/s00220-016-2736-2

We study a class of solutions to the parabolic Ginzburg-Landau equation in dimension 2 or higher, with ill-prepared infinite energy initial data. We show that, asymptotically, the vorticity evolves according to motion by mean curvature in Brakke's weak formulation. Then, we prove that in the plane, point vortices do not move in the original time scale. These results extend the works of Bethuel, Orlandi and Smets (Ann Math (2) 163(1):37-163, 2006; Duke Math J 130(3):523-614, 2005) to infinite energy data; they allow us to consider point vortices on a lattice (in dimension 2), or filament vortices of infinite length (in dimension 3).

• 出版日期2017-3