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

Yoshihiro Shibata, Senjo Shimizu

Research output: Contribution to journalArticlepeer-review

8 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 languageEnglish
Pages (from-to)151-155
Number of pages5
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume81
Issue number9
DOIs
Publication statusPublished - 2005 Nov

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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