On the $L_1$-maximal regularity in the study of free boundary problem for the compressible fluid flows

TL;DR

This paper establishes the $L_1$ maximal regularity for solutions to linearized Stokes equations with free boundary conditions, providing a key analytical tool for studying free boundary problems in compressible fluid flows.

Contribution

It proves the $L_1$ maximal regularity for the linearized Stokes equations with free boundary conditions, advancing the mathematical understanding of free boundary problems in fluid dynamics.

Findings

Proved $L_1$ maximal regularity for the linearized Stokes equations.

Analyzed free boundary conditions in the context of compressible fluids.

Provided a foundation for further studies on free boundary problems.

Abstract

In this paper, we consider the Stokes equations with non-homogeneous free boundary conditions, which is obtained by the linearization procedure of the free boundary problem of the Navier-Stokes equations describing the viscous compressible fluid flows. We prove the $L_1$ maximal regularity of solutions to this Stokes equations.