A remark on the Cauchy problem for the 2D Gross-Pitaevskii equation with nonzero degree at infinity

Abstract

We prove global well-posedness for the Gross-Pitaevskii equation on the plane for classes of initial data having nonzero topological degree at infinity and therefore infinite Ginzburg-Landau energy. These classes allow us to consider arbitrary configurations of vortices as initial data. Our work follows recent results of Patrick Gérard [9] and Clément Gallo [4], where the finite energy regime is treated.