On the R-sectoriality and the initial boundary value problem for the viscous compressible fluid flow

Yuko Enomoto, Yoshihiro Shibata

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

In this paper, we prove the R-sectoriality of the resolvent problem for the boundary value problem of the Stokes operator for the compressible viscous fluids in a general domain, which implies the generation of analytic semigroup and the maximal Lp-Lq regularity for the initial boundary value problem of the Stokes operator. Combining our linear theory with fixed point arguments in the Lagrangian coordinates, we have a local in time unique existence theorem in a general domain and a global in time unique existence theorem for some initial data close to a constant state in a bounded domain for the initial boundary value problem of the Navier-Stokes equations describing the motion of compressible viscous fluids. All the results obtained in this paper were announced in Enomoto-Shibata [12].

Original languageEnglish
Pages (from-to)441-505
Number of pages65
JournalFunkcialaj Ekvacioj
Volume56
Issue number3
DOIs
Publication statusPublished - 2013 Dec 27

Keywords

  • Analytic semigroup
  • Compressible viscous fluid
  • Exponential stability
  • General domain
  • Global in time unique existence theorem
  • Local in time unique existence theorem
  • Maximal L-L regularity
  • Navier-Stokes equations
  • R-sectoriality
  • Stokes equations

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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