The Effect of Transport Noise on Interface Formulation

The paper discusses a mass conserving Allen–Cahn equation with a small parameter \(\epsilon >0\) perturbed by transport type noise involving the smeared noise \({\dot{w}}^\epsilon _i\) (formally converging to white noise \({\dot{w}}_i\)), and investigate its sharp interface limit as \(\epsilon \rightarrow 0\). We restrict our discussion over the two-dimensional domain to construct the hypersurface driven by the stochastic term appearing due to the contribution from the transport term when \(\epsilon \rightarrow 0\). We make use of asymptotic expansion method to discuss the sharp interface limit.