标题： 二维随机Navier-Stokes方程在移动域上的强适定性 显示英文标题

标题： Strong well-posedness of the two-dimensional stochastic Navier-Stokes equation on moving domains

摘要： 本文中，我们在具有乘性噪声的二维随机Navier-Stokes方程在移动区域上建立了强（$H^1$）适定性。 由于非局部效应，此方程表现出“分段”的变分设定。 也就是说，该方程的整体适定性被分解为在每个小时间区间上的变分设定下的随机偏微分方程（SPDEs）的适定性。 我们首先检查每个时间区间的适定性，这些区间没有（非齐次）强制性。 随后，我们给出了时间区间的下界长度估计，这使得我们可以得到整体适定性。 显示英文摘要

摘要： In this paper, we establish the strong($H^1$) well-posedness of the two dimensional stochastic Navier-Stokes equation with multiplicative noise on moving domains. Due to the nonlocality effect, this equation exhibits a ``piecewise" variational setting. Namely the global well-posedness of this equation is decomposed into the well-posedness of a family of stochastic partial differential equations(SPDEs) in the variational setting on each small time-interval. We first examine the well-posedness on each time interval, which does not have (nonhomogeneous) coercivity. Subsequently, we give an estimate of lower bound of length of the time-interval, which enables us to achieve the global well-posedness.