Local well-posedness of the Schrödinger flow into \mathbbS² with natural boundary conditions

2025/12/29 by Bo Chen, Chen, Bo, Youde Wang +1
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Gas Dynamics and Kinetic Theory

paper · doi:10.48550/arxiv.2512.23201

Abstract

In this paper, we develop a new approximation scheme to solve the local well-posedness problem for the Schrödinger flow into the standard unit 2-sphere \mathbbS²⊂ℝ³ (i.e., the Landau-Lifshitz equation) with natural boundary conditions.

Citations

• Periodic Schrödinger map flow on Kähler manifolds
• Smooth solutions to the Schrödinger flow for maps from smooth bounded domains in Euclidean spaces into \mathbbS²
• On global dynamics of Schrödinger map flows on hyperbolic planes near harmonic maps
• Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional
• Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane Under the Schrödinger Maps Evolution
• Mathematical analysis of weak and strong solutions to an evolutionary\n model for magnetoviscoelasticity
• Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: Energy critical case
• Blow up dynamics for equivariant critical Schrödinger maps
• Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions
• Global wellposedness in the energy space for the Maxwell-Schrödinger system
• Schrödinger Maps and their associated Frame Systems
• Asymptotic stability of harmonic maps under the Schrödinger flow
• On Schrödinger maps
• Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: High dimensions

Related

• Global well-posedness for 2D radial Schrödinger maps into the sphere
• Smooth solutions to the Schrödinger flow for maps from smooth bounded domains in Euclidean spaces into \mathbbS²
• Global Well-Posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey space
• On Schrödinger Maps
• On well-posedness of the s-Schrödinger maps in the subcritical regime