Ergodicity of Stochastic Curve Shortening Flow in the Plane
Probability
2010-03-11 v1
Abstract
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
Keywords
Cite
@article{arxiv.1003.2074,
title = {Ergodicity of Stochastic Curve Shortening Flow in the Plane},
author = {A. Es-Sarhir and M. -K. von Renesse},
journal= {arXiv preprint arXiv:1003.2074},
year = {2010}
}
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