On uniqueness for Schrödinger maps with low regularity large data. (English) Zbl 1463.35468

Summary: We prove that the solutions to the initial-value problem for the 2-dimensional Schrödinger maps are unique in \[C_tL^\infty_x\cap L^\infty_t(\dot{H}^1_x\cap\dot{H}^2_x).\] For the proof, we follow H. McGahagan’s argument [Commun. Partial Differ. Equations 32, No. 3, 375–400 (2007; Zbl 1122.35138)] with improving its technical part, combining V. I. Yudovich’s argument [Zh. Vychisl. Mat. Mat. Fiz. 3, 1032–1066 (1963; Zbl 0129.19402)].


35Q55 NLS equations (nonlinear Schrödinger equations)
35Q60 PDEs in connection with optics and electromagnetic theory
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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