On Uniqueness for Schr\"odinger maps with low regularity large data

TL;DR

This paper establishes the uniqueness of solutions for 2D Schr"odinger maps with low regularity large data, advancing the understanding of their well-posedness in specific function spaces.

Contribution

It improves existing techniques by combining McGahagan's and Yudovich's arguments to prove uniqueness under low regularity conditions.

Findings

Solutions are unique in specified function spaces.

Enhanced proof techniques for Schr"odinger maps.

Applicable to large initial data with low regularity.

Abstract

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