The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity

For rather general nonlinearities, we prove that defocusing nonlinear Schrödinger equations in ℝ n (n ≤ 4), with non-vanishing initial data at infinity u 0, are globally well-posed in u 0 + H 1. The same result holds in an exterior domain in ℝ n , n = 2, 3.