On Uniqueness for Schrödinger maps with low regularity large data

Abstract

We prove that the solutions to the initial-value problem for 2-dimensional Schrödinger maps are unique in $C_t{L}_x^{\infty }\cap L_t^{\infty }({\dot{H}}_x^1\cap {\dot{H}}_x^2)$. For the proof, we follow McGahagan's argument with improving its technical part, combining Yudovich's argument.

13 pages