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

TL;DR

This paper establishes conditions for initial data that ensure the existence and uniqueness of short-time regular solutions to a nonlinear Landau-Lifshitz-Gilbert system with spin-polarized transport, a complex coupled parabolic PDE.

Contribution

It provides a detailed description of compatibility conditions for initial data, enabling well-posedness results for this nonlinear coupled system.

Findings

Existence and uniqueness of short-time solutions under specific initial data conditions

Precise compatibility conditions for initial data

Analysis of a nonlinear coupled parabolic system with non-local energy

Abstract

In this paper, we provide a precise description of the compatibility conditions for the initial data so that one can show the existence and uniqueness of regular short-time solution to the Neumann initial-boundary problem of a class of Landau-Lifshitz-Gilbert system with spin-polarized transport, which is a strong nonlinear coupled parabolic system with non-local energy.