We consider the nonlocal Cahn-Hilliard equation with constant mobility and singular potential in three dimensional bounded and smooth domains. This model describes phase separation in binary fluid mixtures. Given any global solution (whose existence and uniqueness are already known), we prove the so-called instantaneous and uniform separation property: any global solution with initial finite energy is globally confined (in the \(L^\infty \) metric) in the interval \([-1+\delta ,1-\delta ]\) on the time interval \([\tau ,\infty )\) for any \(\tau >0\), where \(\delta \) only depends on the norms of the initial datum, \(\tau \) and the parameters of the system. We then exploit such result to improve the regularity of the global attractor for the dynamical system associated to the problem.

我们考虑在三维有界和光滑域中具有恒定迁移率和奇异势的非局部 Cahn-Hilliard 方程。该模型描述了二元流体混合物中的相分离。给定任何全局解（其存在性和唯一性已知），我们证明所谓的瞬时均匀分离性质：任何具有初始有限能量的全局解都被全局限制（在\(L^\infty \)度量中）对于任何\(\tau >0\) ，时间间隔 \([\tau ,\infty )\) 上的间隔\ ([ -1+\delta ,1-\delta ]\)，其中\(\delta \ )仅取决于初始数据范数\(\tau \)和系统参数。然后，我们利用这样的结果来改善与问题相关的动力系统的全局吸引子的规律性。