Smooth local solutions to the Schrödinger flow for maps from a smooth bounded domain $Ω\subset \mathbb{R}^3$ into $\mathbb{S}^2$

Bo Chen, Youde Wang

Published 2021-11-29, updated 2022-04-12Version 2

In this paper, we show the existence and uniqueness of short-time very regular or smooth solution to the initial-Neumann boundary value problem of the Schr\"{o}dinger flow for maps from a smooth bounded domain $\Omega\subset \mathbb{R}^3$ into $\mathbb{S}^2$ in the scale of Sobolev spaces. We provide a precise description of the compatibility conditions at the boundary for the initial data.