二维Landau-Lifshitz-Darwin耦合模型带小初值的整体光滑解

Global Smooth Solutions for the 2-Dimensional Landau-Lifshitz Equations coupled with Darwin model with Small Initial Data

摘要: 通过利用~Galerkin方法得到了周期边值问题的局部光滑解，然后在小初值的条件下对光滑解做关于时间的整体先验估计，得到了二维~Landau-Lifshitz-Darwin方程组在小初值条件下的整体光滑解.

Abstract: The local existence of smooth solution with the periodic initial value condition is firstly obtained by using Galerkin method. Based on it, the global existence of the smooth solution with small initial data is further derived by making a priori estimate globally in time.