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

    29 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

    Fingerprint

    Stokes Operator
    Compressible Fluid
    Compressible Flow
    Viscous Fluid
    Existence Theorem
    Initial-boundary-value Problem
    Fluid Flow
    Lagrangian Coordinates
    Analytic Semigroup
    Resolvent
    Bounded Domain
    Navier-Stokes Equations
    Regularity
    Fixed point
    Boundary Value Problem
    Imply
    Motion

    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

    • Algebra and Number Theory
    • Analysis
    • Geometry and Topology

    Cite this

    On the R-sectoriality and the initial boundary value problem for the viscous compressible fluid flow. / Enomoto, Yuko; Shibata, Yoshihiro.

    In: Funkcialaj Ekvacioj, Vol. 56, No. 3, 2013, p. 441-505.

    Research output: Contribution to journalArticle

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