Asymptotic behaviors of Landau-Lifshitz flows from \(\mathbb {R}^2\) to Kähler manifolds

DOI10.1007/s00526-017-1182-0zbMath1375.35045arXiv1605.01245OpenAlexW2964009624MaRDI QIDQ2406060

Lifeng Zhao, Ze Li

Publication date: 26 September 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.01245

zbMATH Keywords

asymptotic behaviorbubbling theoremKahler manifoldsLandau-Lifschitz flow

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Heat and other parabolic equation methods for PDEs on manifolds (58J35) PDEs in connection with statistical mechanics (35Q82)

Related Items (2)

Convergence to harmonic maps for the Landau-Lifshitz flows between two dimensional hyperbolic spaces ⋮ Asymptotic behaviors for nonlinear dispersive equations with damping or dissipative terms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equivariant Schrödinger maps in two spatial dimensions: the \(\mathbb{H}^2\) target
• Equivariant Schrödinger maps in two spatial dimensions
• Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem
• Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces
• Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schrödinger maps on \(\mathbb R^2\)
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Boundary regularity and the Dirichlet problem for harmonic maps
• On the global well-posedness of the one-dimensional Schrödinger map flow
• Asymptotic stability of harmonic maps under the Schrödinger flow
• The Cauchy problem for Schrödinger flows into Kähler manifolds
• Energy dispersed large data wave maps in \(2+1\) dimensions
• Regularity of wave-maps in dimension \(2+1\)
• A regularity theory for harmonic maps
• On the evolution of harmonic mappings of Riemannian surfaces
• Existence and uniqueness of smooth solution for system of ferromagnetic chain
• Finite-time blow-up of the heat flow of harmonic maps from surfaces
• Pseudo-holomorphic maps and bubble trees
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
• The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
• Local Schrödinger flow into Kähler manifolds
• On the continuous limit for a system of classical spins
• Uniqueness and bubbling of the 2-dimensional Landau-Lifshitz flow
• On singularities of the heat flow for harmonic maps from surfaces into spheres
• Global existence and uniqueness of Schrödinger maps in dimensions \(d\geq 4\)
• Blow up dynamics for equivariant critical Schrödinger maps
• The problem of Plateau on a Riemannian manifold
• Geometric Renormalization Below the Ground State
• On the Landau-Lifshitz equation in dimensions at most four
• An Approximation Scheme for Schrödinger Maps
• Schrödinger flow near harmonic maps
• On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• Schrödinger maps
• Existence of Partially Regular Solutions for Landau–Lifshitz Equations in ℝ³
• Schrodinger Maps and their Associated Frame Systems
• The construction of a partially regular solution to the Landau–Lifshitz–Gilbert equation in

This page was built for publication: Asymptotic behaviors of Landau-Lifshitz flows from \(\mathbb {R}^2\) to Kähler manifolds