L p-L q maximal regularity and viscous incompressible flows with free surface

Yoshihiro Shibata; Senjo Shimizu

doi:10.3792/pjaa.81.151

L _p-L _q maximal regularity and viscous incompressible flows with free surface

Yoshihiro Shibata^*, Senjo Shimizu

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We prove the L _p-L _q maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. And as an application, we consider a free boundary problem for the Navier-Stokes equation. We prove a locally in time unique existence of solutions to this problem for any initial data and a globally in time unique existence of solutions to this problem for some small initial data.

Original language	English
Pages (from-to)	151-155
Number of pages	5
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	81
Issue number	9
DOIs	https://doi.org/10.3792/pjaa.81.151
Publication status	Published - 2005 Nov

Keywords

Free boundary problem
Maximal regularity
Navier-Stokes equations
Neumann boundary condition
Stokes equations

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.3792/pjaa.81.151

Cite this

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KW - Free boundary problem

KW - Maximal regularity

KW - Navier-Stokes equations

KW - Neumann boundary condition

KW - Stokes equations

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