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

Helmut Abels; Andreas Marquardt

doi:10.3934/dcdss.2020467

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2021, Volume 14, Issue 11: 3973-3987. Doi: 10.3934/dcdss.2020467 open access

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

Helmut Abels^, and
Andreas Marquardt

Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany

^* Corresponding author: Helmut Abels
^* Corresponding author: Helmut Abels

Received: May 31, 2020

Revised: August 31, 2020

Early access: November 2020

Published: November 2021

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Abstract

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.

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Mathematics Subject Classification: Primary: 76T99; Secondary: 35Q30, 35Q35, 35R35, 76D05, 76D45.

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References

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