Schrödinger maps to a Kähler manifold in two dimensions

2025/12/22 by Benjamin Dodson, Dodson, Benjamin, Jeremy L. Marzuola +1
Mathematics · #35B40 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2512.19559

openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

We prove a global well--posedness and scattering result for Schrödinger maps to a general Kähler manifold with small initial data in a Besov space.

Citations

• Near soliton evolution for 2-equivariant Schrödinger Maps in two space dimensions
• Global solutions for 1D cubic dispersive equations, Part III: the quasilinear Schrödinger flow
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• A controlling norm for energy-critical Schrödinger maps
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• On Schrödinger maps
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Related

• Low-regularity Schrödinger maps, II: global well-posedness in dimensions d≥ 3
• On Schrödinger Maps
• The Cauchy problem for Schrödinger flows into Kähler manifolds
• Global results for Schrödinger Maps in dimensions n ≥ 3
• Schrödinger Maps and their associated Frame Systems