On the $L_{1}$ maximal regularity in the study of free boundary problem for the compressible fluid flows
Abstract
In this paper, we consider the Stokes equations with non-homogeneous free boundary conditions, which are 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 these Stokes equations. This is an extension result of $L_{p}$-$L_{q}$ maximal regularity result obtained by D. Götz and Y. Shibata to the $L_{1}$ in time maximal regularity case.
Fields of Study & Subjects
Navier-Stokes equation solutions
Differential Equations and Boundary Problems
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Journal of the Mathematical Society of Japan
- Volume
- -1
- Issue
- -1
- Pages
- 1–63
- Publication date
- 2 September 2026
- Language
- EN