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.
A weak-strong uniqueness principle for the Mullins-Sekerka equation
Institute of Science and Technology Austria（奥地利科学技术研究所）；Hausdorff Center for Mathematics, Universität Bonn（波恩大学霍尔德夫数学中心）；Faculty of Mathematics, University of Regensburg（雷根斯堡大学数学系）；Westfälische Wilhelms-Universität Münster（明斯特西法利亚威廉大学）
Dynamical stability for the periodic modified Mullins-Sekerka flow
Dipartimento di Matematica, Università degli Studi di Milano（米兰大学数学系）；Institute of Analysis and Scientific Computing, Technische Universität Wien（维也纳工业大学分析与科学计算研究所）
A Structure-Preserving Method of Fundamental Solutions for the Multi-Phase Mullins-Sekerka Flow
Université Claude Bernard Lyon 1, CNRS, Centrale Lyon, INSA Lyon, Université Jean Monnet, ICJ UMR5208（里昂第一大学、法国国家科学研究中心、中央里昂学院、里昂国立应用科学学院、让·莫内大学、ICJ UMR5208）
Functional inequalities and strong Lyapunov functionals for free surface flows in fluid dynamics
This paper is motivated by the study of Lyapunov functionals for four equations describing free surface flows in fluid dynamics: the Hele-Shaw and Mullins-Sekerka equations together with their lubrication approximations, the Boussinesq and thin-film equations. We identify new Lyapunov functionals, including some which decay in a convex manner (these are called strong Lyapunov functionals). For the Hele-Shaw equation and the Mullins-Sekerka equation, we prove that the $L^2$ -norm of the free surface elevation and the area of the free surface are Lyapunov functionals, together with parallel resu…
