  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 systemto 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.
