We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in the case of a $W^{1,1}$ convolution kernel and under homogeneous Neumann conditions. Any type of potential, possibly also of double-obstacle or logarithmic type, is included. Additionally, we highlight variants and extensions to the setting of periodic boundary conditions and viscosity contributions, as well as connections with the general theory of evolutionary convergence of gradient flows.

中文翻译：

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具有W ^1,1核和奇异势的非局部对流Cahn-Hilliard方程的局部渐近性

我们证明了解的存在性，并研究了非局部，对流，Cahn-Hilliard方程的非局部到局部渐近性。 ${\mathrm{w\; ^}}^{\mathrm{1个}，\mathrm{1个}}$卷积核并在均匀诺伊曼条件下。包括任何类型的电位，也可能是双重障碍或对数类型。此外，我们重点介绍了周期性边界条件和粘度贡献的设置的变体和扩展，以及与梯度流演化收敛的一般理论的联系。