On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations

Y. Shibata, S. Shimizu

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fiuidfiow. We show standard resolvent estimates in the Lq framework (1 <q< ∞), applying some kernel estimates to concrete solution formulas. The Volevich trick in [21] plays a fundamental role in estimating solutions.

Original languageEnglish
Pages (from-to)482-499
Number of pages18
JournalMathematische Nachrichten
Volume282
Issue number3
DOIs
Publication statusPublished - 2009 Mar 1

Keywords

  • Free boundary problem
  • Gravity force
  • L framework
  • Resolvent estimate
  • Stokes equation
  • Surface tension

ASJC Scopus subject areas

  • Mathematics(all)

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