LAGRANGIAN FORMULATION, ENERGY ESTIMATES, AND THE SCHRÖDINGER MAP PROBLEM

DOI10.1081/PDE-120016130zbMath1021.35103OpenAlexW2021472909MaRDI QIDQ4796714

Vangelis Stefanopoulos, Manoussos G. Grillakis

Publication date: 5 March 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120016130

zbMATH Keywords

conservation lawsLagrangian formulationSchrödinger mapenergy type estimate

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (11)

Equivariant Schrödinger maps in two spatial dimensions: the \(\mathbb{H}^2\) target ⋮ Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem ⋮ Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution ⋮ The Fukumoto-Moffatt's model in the vortex filament and generalized bi-Schrödinger maps ⋮ Asymptotic stability of harmonic maps under the Schrödinger flow ⋮ An unconstrained Lagrangian formulation and conservation laws for the Schrödinger map system ⋮ Explicit blow-up solutions to the Schrödinger maps from R2 to the hyperbolic 2-space H2 ⋮ Local nonautonomous Schrödinger flows on Kähler manifolds ⋮ Blow up dynamics for equivariant critical Schrödinger maps ⋮ SOME EXACT BLOWUP SOLUTIONS TO MULTIDIMENSIONAL SCHRÖDINGER MAP EQUATION ON HYPERBOLIC SPACE AND CONE ⋮ Uniqueness of the Modified Schrödinger Map inH^3/4+ε(ℝ²)

Cites Work

• Unnamed Item
• The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
• Schrödinger maps
• On the integrability of the inhomogeneous spherically symmetric Heisenberg ferromagnet in arbitrary dimensions
• A soliton on a vortex filament

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