随机Landau-Lifshitz-Gilbert方程的弱解
Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation
摘要：
研究了填充有界三维区域的铁磁体在乘性空间相关噪声扰动下的Landau-Lifshitz-Gilbert方程。证明了取值于球面$\mathbb S^2$的弱鞅解的存在性。讨论了弱解的正则性。一些正则性结果是新的，即使是确定性的Landau-Lifshitz-Gilbert方程。
英文摘要：
The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative space-dependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere $\mathbb S^2$. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert equation.
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