Global well-posedness for 2D radial Schrödinger maps into the sphere

2011/05/27 by Stephen J. Gustafson, Gustafson, Stephen, Eva Koo +1 · 2 citations
Mathematics · #35Q55 #53C44 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1105.5659

openalex publication_date 2011/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove global well-posedness for a cubic, non-local Schrödinger equation with radially-symmetric initial data in the critical space L²(\R²), using the framework of Kenig-Merle and Killip-Tao-Visan. As a consequence, we obtain a global well-posedness result for Schrödinger maps from \R² into §² (Landau-Lifshitz equation) with radially symmetric initial data (with no size restriction).

Cited by

• Global wellposedness of the equivariant Chern-Simons-Schrödinger equation
• Bilinear Strichartz estimates for the Schrödinger map problem

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