平面随机曲线缩短流的遍历性
Ergodicity of Stochastic Curve Shortening Flow in the Plane
摘要：
研究了二维布朗速度场中（1+1）维界面的中曲率运动模型。对于模型的适定性，我们在Krylov Rozovskii变分框架下证明了退化非线性随机发展方程解的存在唯一性，用一个Lyapunov型条件取代了标准的非线性假设.利用Komorowski，Peszat和Szarek关于马尔可夫半群的下界技术，建立了加性噪声情形下的遍历性
英文摘要：
We study a model of the motion by mean curvature of an (1+1) dimensional interface in a 2D Brownian velocity field. For the well-posedness of the model we prove existence and uniqueness for certain degenerate nonlinear stochastic evolution equations in the variational framework of Krylov Rozovskii, replacing the standard coercivity assumption by a Lyapunov type condition. Ergodicity is established for the case of additive noise, using the lower bound technique for Markov semigroups by Komorowski, Peszat and Szarek
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
