Remarks on local theory for Schrödinger maps near harmonic maps

DOI10.2996/KMJ/1594313555zbMath1447.35284arXiv1806.02365OpenAlexW3041283062MaRDI QIDQ783757

Ikkei Shimizu

Publication date: 4 August 2020

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.02365

zbMATH Keywords

uniquenesslocal well-posednessCoulomb gaugeSchrödinger mapsmodified Schrödinger maps

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (1)

Local well-posedness of the Landau–Lifshitz equation with helicity term

Cites Work

• Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem
• Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schrödinger maps on \(\mathbb R^2\)
• Asymptotic stability of harmonic maps under the Schrödinger flow
• The Cauchy problem for Schrödinger flows into Kähler manifolds
• Blow up dynamics for equivariant critical Schrödinger maps
• An Approximation Scheme for Schrödinger Maps

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