Maximal regularity of Stokes problem with dynamic boundary condition -- Hilbert setting

TL;DR

This paper establishes the maximal regularity of weak solutions for the evolutionary Stokes problem with dynamic boundary conditions in a Hilbert space setting, using sectorial operator theory.

Contribution

It demonstrates that the associated operator is sectorial and generates an analytic semigroup, enabling maximal regularity results for the problem.

Findings

Proves maximal regularity of weak solutions in time.

Shows the operator is sectorial and generates an analytic semigroup.

Provides a functional analytic framework for the problem.

Abstract

For the evolutionary Stokes problem with dynamic boundary conditions, we show the maximal regularity of weak solutions in time. Due to the characterization of $R$-sectorial operators on Hilbert spaces, the proof reduces to identifying the appropriate functional analytic setting and proving that the corresponding operator is sectorial, i.e., that it generates an analytic semigroup.