Uniqueness of Schrodinger flow via energy inequality

TL;DR

This paper proves the uniqueness of energy solutions for the Schrödinger flow in the whole space, assuming the existence of a smooth solution within the same energy class.

Contribution

It establishes a uniqueness result for Schrödinger flow energy solutions under the condition of a smooth solution's presence.

Findings

Uniqueness of energy solutions for Schrödinger flow in R^n.

Conditional on the existence of a smooth solution.

Applicable to the Cauchy problem in the whole space.

Abstract

In this short note, we show a uniqueness result of the energy solutions for the Cauchy problem of Schrodinger flow in the whole space $R^n$ provided there is a smooth solution in the energy class.