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Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations pp 305–321Cite as

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About Compressible Viscous Fluid Flow in a 2-dimensional Exterior Domain

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 221))

Abstract

We report our results [5, 6, 7] concerning a global in time unique existence theorem of strong solutions to the equation describing the motion of compressible viscous fluid flow in a 2-dimensional exterior domain for small initial data and some decay properties of the analytic semigroup associated with Stokes operator of compressible viscous fluid flow in a 2-dimensional exterior domain.Our results are an extension of the works due to Matsumura and Nishida [13] and Kobayashi and Shibata [10] in a 3-dimensional exterior domain to the 2-dimensional case.W e also discuss some analytic semigroup approach to the compressible viscous fluid flow in a bounded domain, which was first investigated by G.S trömer [20, 21, 22].

Mathematics Subject Classification (2000). 35Q30, 76N10.

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Author information

Authors and Affiliations

  1. Fukasaku 307 Minuma-ku, Saitama-shi, Saitama, 337-8570, Japan

    Yuko Enomoto

  2. Ohkubo 3-4-1 Shinjuku-ku, Tokyo, 169-8555, Japan

    Yoshihiro Shibata

Authors
  1. Yuko Enomoto
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  2. Yoshihiro Shibata
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Corresponding author

Correspondence to Yuko Enomoto .

Editor information

Editors and Affiliations

  1. , Abt. Mathematik V, Universität Ulm, Ulm, 89069, Germany

    Wolfgang Arendt

  2. Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA

    Joseph A. Ball

  3. Institut für Mathematik, AG Modellierung, Numerik und, TU Berlin, Straße des 17 Juni 136, Berlin, 10623, Berlin, Germany

    Jussi Behrndt

  4. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Karl-Heinz Förster

  5. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Volker Mehrmann

  6. , Institut für Mathematik, TU Ilmenau, Weimarer Str. 25, Ilmenau, 98693, Thüringen, Germany

    Carsten Trunk

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Enomoto, Y., Shibata, Y. (2012). About Compressible Viscous Fluid Flow in a 2-dimensional Exterior Domain. In: Arendt, W., Ball, J., Behrndt, J., Förster, KH., Mehrmann, V., Trunk, C. (eds) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0297-0_17

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