带有Gilbert阻尼项的Landau-Lifshitz铁磁链方程解的最佳衰减率

Optimal rate of decay for solutions for the Landau-Lifshitz equation with Gilbert damping for ferromagnetism

主要研究带有Gilbert阻尼项的Landau-Lifshitz铁磁链方程的柯西问题.当初值的一阶导数适当小时,基于加权能量估计,证明了强解的整体存在性并且给出了解的最优的L2和L∞衰减估计.

In this paper we study the Cauchy problem for the important Landau-Lifshitz equation with Gilbert damping for ferromagnetism. We establish the global existence of strong solution and at the same time we give some decay estimates of solutions which are indeed optimal. Our analysis is based on the a priori weighted energy estimate methods. And only the smallness of the first derivatives of the initial data is assumed.