论文标题
Landau-Lifshitz方程式的本地适应性术语
Local well-posedness for the Landau-Lifshitz equation with helicity term
论文作者
论文摘要
我们考虑使用helicity项（手性相互作用项）的Landau-Lifshitz方程的初始值问题，这是由Dzyaloshinskii-Moriya相互作用引起的。我们证明，它在空间中的本地时间很好，$ \ bar {k} +h^s $ for $ s \ ge 3 $，$ s \ in \ mathbb {z} $和$ \ bar {k} = {} = {}^t（0,0,0,1）$。我们还表明，如果我们进一步假设该解决方案是恒定地图的同型，那么本地供应良好，则在$ \ bar {k} + h^s $中保留$ s> 2 $，in \ mathbb {r} $。我们的证明是通过修改后的Schrödinger图方程进行的分析。
We consider the initial value problem for the Landau-Lifshitz equation with helicity term (chiral interaction term), which arises from the Dzyaloshinskii-Moriya interaction. We prove that it is well-posed locally-in-time in the space $\bar{k} +H^s$ for $s\ge 3$ with $s\in \mathbb{Z}$ and $\bar{k}={}^t(0,0,1)$. We also show that if we further assume that the solution is homotopic to constant maps, then local well-posedness holds in the space $\bar{k} + H^s$ for $s>2$ with $s\in \mathbb{R}$. Our proof is base on the analysis via the modified Schrödinger map equation.
