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

2020/12/27 by Jitao Xu, Lifeng Zhao, Xu, Jitao +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2012.13879

openalex publication_date 2020/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the energy critical 1-equivariant Landau-Lifschitz flow mapping ℝ² to \mathbbS² 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.

Citations

• Harmonic Mappings of Riemannian Manifolds
• Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: Energy critical case

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