We consider the stochastic nonlinear Schrödinger equations on a half-line under Dirichlet brown-noise boundary conditions. We establish the global existence and uniqueness of solutions to the initial-boundary value problem with values in H¹. We are also interested in the regularity behavior of solutions near the origin, where the boundary data are highly irregular.

中文翻译：

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具有Dirichlet噪声边界条件的随机Schrödinger方程

我们考虑在Dirichlet棕色噪声边界条件下半线上的随机非线性Schrödinger方程。我们建立了H ^1中初值问题的整体存在性和解的唯一性。我们也对原点附近解的规则性行为感兴趣，原点附近的边界数据高度不规则。