Ergodicity of Stochastic Curve Shortening Flow in the Plane

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

arXiv comment15

References in corpus (1)

• Tightness for a stochastic Allen--Cahn equation

Cited by in corpus (4)

• Tightness for a stochastic Allen--Cahn equation
• Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts
• Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow
• Convergence of invariant measures for singular stochastic diffusion equations