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with initial data u(0, x) = u0(x), ut(0, x) = u1(x), in the case when x ∈ R and the target is the unit sphere S (embedded in R), n ≥ 2. Thus u : Rt ×Rx → S and we have the additional constraint |u| = 1. For this problem several results of global well-posedness are available under suitable smallness assumptions on the initial data (see [4], [12], [13], [7]). Moreover, the existence of a global weak solution in H is known ([6], [14], [1]) and the existence and uniqueness

On Lipschitz continuity of the solution map for two-dimensional wave maps