On the maximal L p-L q regularity of the Stokes problem with first order boundary condition; model problems

Yoshihiro Shibata, Senjo Shimizu

Research output: Contribution to journalArticle

21 Citations (Scopus)


In this paper, we proved the generalized resolvent estimate and the maximal L p-L q regularity of the Stokes equation with first order boundary condition in the half-space, which arises in the mathematical study of the motion of a viscous incompressible one phase fluid flow with free surface. The core of our approach is to prove the R boundedness of solution operators defined in a sector Σ ∈,γ0 = {λ ∈ C \ {0}

Original languageEnglish
Pages (from-to)561-626
Number of pages66
JournalJournal of the Mathematical Society of Japan
Issue number2
Publication statusPublished - 2012 Oct 9



  • Gravity force
  • Half space problem
  • Maximal regularity
  • Resolvent estimate
  • Stokes equation
  • Surface tension

ASJC Scopus subject areas

  • Mathematics(all)

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