Tightness for a stochastic Allen--Cahn equation

Abstract

We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds and prove tightness of of solutions in the sharp interface limit, and show convergence to phase-indicator functions.

27 pages, final Version to appear in "Stochastic Partial Differential Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new. It replaces and simplifies the old propositions 6.4-6.6

References in corpus (2)

• On the short time asymptotic of the stochastic Allen-Cahn equation
• Ergodicity of Stochastic Curve Shortening Flow in the Plane

Cited by in corpus (6)

• Ergodicity of Stochastic Curve Shortening Flow in the Plane
• Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation
• Generation of fine transition layers and their dynamics for the stochastic Allen--Cahn equation
• Vortices in a Stochastic Parabolic Ginzburg-Landau Equation
• Fully Discrete Mixed Finite Element Methods for the Stochastic Cahn-Hilliard Equation with Gradient-type Multiplicative Noise
• On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces