On the $\mathcal{R}$-Sectoriality and the Initial Boundary Value Problem for the Viscous Compressible Fluid Flow

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Bibliographic Information

Other Title
  • On the R-sectoriality and initial boundary value problem for the viscous compressible fluid flow
  • On the R-sectoriality and the initial boundary value problem for the viscous compressible fluid flow
  • On the R-sectoriality and its application to some mathematical study of the viscous compressible fluids
  • On the R-sectoriality and its application to some mathematical viscous compressible fluids
  • On the $\mathcalR$-sectoriality and its application to some mathematical study of the viscous compressible fluids,

Abstract

In this paper, we prove the $\mathcal{R}$-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].

Journal

  • Funkcialaj Ekvacioj

    Funkcialaj Ekvacioj 56 (3), 441-505, 2013

    Division of Functional Equations, The Mathematical Society of Japan

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