Blowup dynamics for smooth equivariant solutions to energy critical Landau-Lifschitz flow

In this paper, we study the energy critical 1-equivariant Landau-Lifschitz flow mapping R2 to S2 with arbitrary given coefficients ρ1∈R,ρ2>0. We prove that there exists a codimension one smooth well-localized set of initial data arbitrarily close to the ground state which generates type-II finite...

Full description

Saved in:
Bibliographic Details
Published in:Journal of functional analysis 2025-01, Vol.288 (2), p.110704, Article 110704
Main Authors: Xu, Jitao, Zhao, Lifeng
Format: Article
Language:English
Subjects:
Energy critical
Landau-Lifschitz flow
Schrödinger map
Type-II blowup
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study the energy critical 1-equivariant Landau-Lifschitz flow mapping R2 to S2 with arbitrary given coefficients ρ1∈R,ρ2>0. We prove that there exists a codimension one smooth well-localized set of initial data arbitrarily close to the ground state which generates type-II finite-time blowup solutions, and give a precise description of the corresponding singularity formation. In our proof, both the Schrödinger part and the heat part play important roles in the construction of approximate solutions and the mixed energy/Morawetz functional. However, the blowup rate is independent of the coefficients.
ISSN:0022-1236
DOI:10.1016/j.jfa.2024.110704