On a linearized Mullins-Sekerka/Stokes system for two-phase flows

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-Sobolev spaces with the aid of a maximal regularity result for non-autonomous abstract linear evolution equations.</p>