Very regular solution to Landau-Lifshitz-Gilbert system with spin-polarized transport

DOI10.1007/s11464-021-0209-1zbMath1528.35156arXiv2105.06616OpenAlexW4385074008MaRDI QIDQ6058649

You-De Wang, Bo Chen

Publication date: 1 November 2023

Published in: Frontiers of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.06616

zbMATH Keywords

Galerkin approximation methodauxiliary approximation equationcompatibility conditions of the initial dataLandau-Lifshitz system with spin-polarized transportvery regular solution

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Statistical mechanics of magnetic materials (82D40) Time-dependent Schrödinger equations and Dirac equations (35Q41) Integro-partial differential equations (35R09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Quasilinear parabolic equations (35K59)

Related Items

Existence and uniqueness of local regular solution to the Schrödinger flow from a bounded domain in \(\mathbb{R}^3\) into \(\mathbb{S}^2\), Smooth local solutions to Schrödinger flows with damping term for maps into symplectic manifolds

Cites Work

• Unnamed Item
• Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces
• Schrödinger flow for maps into Kähler manifolds
• Current-induced magnetization dynamics. Global existence of weak solutions
• Landau-Lifschitz-Gilbert equation with applied electric current
• Compact sets in the space \(L^ p(0,T;B)\)
• Existence and uniqueness of smooth solution for system of ferromagnetic chain
• Schrödinger flow of maps into symplectic manifolds
• The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
• Uhlenbeck compactness
• Local Schrödinger flow into Kähler manifolds
• Very regular solutions for the Landau-Lifschitz equation with electric current
• Mathematical tools for the study of the incompressible Navier-Stokes equations and related models
• On the continuous limit for a system of classical spins
• Regular solutions for Landau-Lifschitz equation in a bounded domain.
• Schrödinger flow on Hermitian locally symmetric spaces
• Global weak solutions to Landau-Lifshitz equations into compact Lie algebras
• Global weak solutions to Landau-Lifshtiz systems with spin-polarized transport
• Partial regularity to the Landau-Lifshitz equation with spin accumulation
• Global existence and uniqueness of Schrödinger maps in dimensions \(d\geq 4\)
• Low-regularity Schrödinger maps. II: Global well-posedness in dimensions \(d \geq 3\)
• Spin-polarized transport: existence of weak solutions
• Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional
• Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions
• On the Landau-Lifshitz equation in dimensions at most four
• On Schrödinger maps
• On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness
• Heisenberg chain systems from compact manifolds into S2
• On Landau-Lifshitz’ equations for ferromagnetism
• Finite Time singularity of the Landau-Lifshitz-Gillbert Equation
• Global Results for Schrödinger Maps in Dimensionsn ≥ 3