Local Theory of Yang-Mills-Higgs-Schr\"{o}dinger Flow

TL;DR

This paper investigates two Hamiltonian flows, establishing local existence for the Yang-Mills-Higgs-Schrödinger flow and uniqueness for the A-Schrödinger flow, contributing to the understanding of their mathematical properties.

Contribution

It provides the first local existence result for the Yang-Mills-Higgs-Schrödinger flow and proves uniqueness for the A-Schrödinger flow, advancing the theoretical framework of these flows.

Findings

Local existence for Yang-Mills-Higgs-Schrödinger flow

Uniqueness for A-Schrödinger flow

Mathematical analysis of Hamiltonian flows

Abstract

In this article, we study two Hamiltonian type flows: Yang-Mills-Higgs-Schr\"odinger flow and $A$-Schr\"odinger flow. For the first one, we only obtain local existence. However, the uniqueness follows from classical tricks for the second one.