Global existence and uniqueness of Schrödinger maps in dimensions d≥ 4

2006/07/23 by Ioan Bejenaru, I. Bejenaru, Bejenaru, I. +6
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.math/0607579

Added references on orthonormal frames

openalex publication_date 2006/07/23 · arxiv created 2006/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In dimensions d≥ 4, we prove that the Schrödinger map initial-value problem admits global (in time) solutions for smooth data with small norm in the critical Sobolev space.

Citations

• Space‐time estimates for null forms and the local existence theorem
• On Schrödinger Maps
• Global well-posedness of the Benjamin-Ono equation in low-regularity spaces

Related

• Global Schrödinger maps
• Low-regularity Schrödinger maps, II: global well-posedness in dimensions d≥ 3
• Global results for Schrödinger Maps in dimensions n ≥ 3
• Global well-posedness for the Schrödinger map problem with small Besov norm
• Conditional global regularity of Schrödinger maps: sub-threshold dispersed energy