The Yang-Mills-Higgs heat flow on \(\mathbb{R}^ 3\)
type: Item
instance of: scholarly article
title: The Yang-Mills-Higgs heat flow on \(\mathbb{R}^ 3\)
zbMATH Open document ID: 0778.35048
author: Andrew Hassell
published in: Journal of Functional Analysis
publication date: 1993-04-28T00:00:00Z
review text: The purpose of this paper is to study the `heat flow' of the Lagrangian, that is, the evolution equation \(\partial_ t(A,\varphi)=- \text{grad}({\mathcal L})\) and show reasonable conditions under which it converges to a monopole. The conditions arrived at by investigations in steps, are: i) short time existence of the flow, (ii) evolution equations for various quantities, (iii) long time existence of the flow, (iv) an analysis of the decay solutions of the model problem \(\partial_ tu=\Delta u\), and finally (v) proof of the power law decay of the Bogomolny tensor along with all its derivatives and convergence of \((A,\varphi)\). The main technical tools used are the parabolic maximum principle, and Sobolev and interpolation inequalities.
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 152049
zbMATH Keywords: Yang-Mills-Higgs action
zbMATH Keywords: heat flow
zbMATH Keywords: Bogomolny tensor
zbMATH Keywords: parabolic maximum principle
zbMATH Keywords: interpolation inequalities
MaRDI profile type: Publication
full work available at URL: jfan.1993.1020
OpenAlex ID: W2000468128
DOI: 10.1006/JFAN.1993.1020
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description: scientific article; zbMATH DE number 152049