Regularity Analysis for Stochastic Complex Landau--Ginzburg Equation with Dirichlet White-Noise Boundary Conditions

Abstract

We consider the stochastic nonlinear Landau--Ginzburg equations on the half-line with Dirichlet white-noise boundary conditions. We establish the local existence and uniqueness of the solution to the initial-boundary value probem with values in an appropriate weighted space. We are also interested in the regularity behavior of the solution, especially near the origin, where the boundary data are highly irregular.