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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.
Clément Gallo (Wed,) studied this question.
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