The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions

被引：7

作者：

Gutierrez, Susana ^{[1
]}

de Laire, Andre ^{[2
]}

机构：

[1] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

[2] Univ Lille, CNRS, INRIA, UMR 8524,Lab Paul Painleve, F-59000 Lille, France

来源：

NONLINEARITY | 2019年 / 32卷 / 07期

基金：

英国工程与自然科学研究理事会;

关键词：

Landau-Lifshitz-Gilbert equation; discontinuous initial data; stability; self-similar solutions; dissipative Schrodinger equation; complex Ginzburg-Landau equation; ferromagnetic spin chain; heat-flow for harmonic maps; LINEAR PARABOLIC EQUATIONS; WELL-POSEDNESS; HEAT-FLOW; EXPANDERS; STABILITY;

D O I：

10.1088/1361-6544/ab1296

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a global well-posedness result for the Landau-Lifshitz equation with Gilbert damping provided that the BMO semi-norm of the initial data is small. As a consequence, we deduce the existence of self-similar solutions in any dimension. In the one-dimensional case, we characterize the self-similar solutions associated with an initial data given by some (S-2-valued) step function and establish their stability. We also show the existence of multiple solutions if the damping is strong enough. Our arguments rely on the study of a dissipative quasilinear Schrodinger equation obtained via the stereographic projection and techniques introduced by Koch and Tataru.

引用

页码：2522 / 2563

页数：42

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