Abstract
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 McGahagan's argument with improving its technical part, combining Yudovich's argument.
Citation
Ikkei Shimizu. "On uniqueness for Schrödinger maps with low regularity large data." Differential Integral Equations 33 (5/6) 207 - 222, May/June 2020. https://doi.org/10.57262/die/1589594448