We study a linearized Mullins-Sekerka/Stokes system in a bounded domain with various boundary conditions. This system plays an important role to prove the convergence of a Stokes/Cahn-Hilliard system to its sharp interface limit, which is a Stokes/Mullins-Sekerka system, and to prove solvability of the latter system locally in time. We prove solvability of the linearized system in suitable $ L^2 $-Sobolev spaces with the aid of a maximal regularity result for non-autonomous abstract linear evolution equations.

中文翻译：

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用于两相流的线性化 Mullins-Sekerka/Stokes 系统

我们在具有各种边界条件的有界域中研究线性化的 Mullins-Sekerka/Stokes 系统。该系统对于证明 Stokes/Cahn-Hilliard 系统收敛到其尖锐的界面极限，即 Stokes/Mullins-Sekerka 系统，以及证明后者系统在局部时间上的可解性起到了重要作用。我们借助非自治抽象线性演化方程的最大正则性结果证明了线性化系统在合适的 $ L^2 $-Sobolev 空间中的可解性。