Hölder convergence of Ginzburg-Landau approximations to the harmonic map heat flow

DOI10.1016/S0362-546X(00)00148-6zbMath1027.35125OpenAlexW1987197014MaRDI QIDQ5953906

Zu Han Liu, Shijin Ding

Publication date: 13 January 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(00)00148-6

zbMATH Keywords

singularitiesharmonic mapssuperconductivityGinzburg-Landau equationsharmonic maps heat flow

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Statistical mechanics of superconductors (82D55) NLS equations (nonlinear Schrödinger equations) (35Q55) Harmonic maps, etc. (58E20)

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Asymptotic behavior of the initial-boundary value problem of Landau-Lifshitz-Schrödinger type ⋮ Robusta priorierror analysis for the approximation of degree-one Ginzburg-Landau vortices ⋮ A uniqueness result on the solution for a Landau-Lifshitz system with penalization ⋮ On an initial-boundary value problem for the p-Ginzburg-Landau system

Cites Work

• On the evolution of harmonic mappings of Riemannian surfaces
• On the evolution of harmonic maps in higher dimensions
• Existence and partial regularity results for the heat flow for harmonic maps
• Asymptotics for the minimization of a Ginzburg-Landau functional
• Uniqueness for the harmonic map flow in two dimensions
• Solutions of Ginzburg-Landau equations and critical points of the renormalized energy
• Evolution of harmonic maps with Dirichlet boundary conditions
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• Partial regularity for weak heat flows into spheres
• Some dynamical properties of Ginzburg-Landau vortices
• Harmonic Mappings of Riemannian Manifolds