About compressible viscous fluid flow in a 2-dimensional exterior domain

Yuko Enomoto; Yoshihiro Shibata

doi:10.1007/978-3-0348-0297-0_17

About compressible viscous fluid flow in a 2-dimensional exterior domain

Yuko Enomoto, Yoshihiro Shibata

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

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. We 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].

Original language	English
Title of host publication	Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 2010
Editors	Wolfgang Arendt, Jussi Behrndt, Volker Mehrmann, Karl-Heinz Förster, Joseph A. Ball, Carsten Trunk
Publisher	Springer International Publishing
Pages	305-321
Number of pages	17
ISBN (Print)	9783034802963
DOIs	https://doi.org/10.1007/978-3-0348-0297-0_17
Publication status	Published - 2012
Externally published	Yes
Event	21st International Workshop on Operator Theory and Applications, 2010 - Berlin, Germany Duration: 2010 Jul 12 → 2010 Jul 16

Publication series

Name	Operator Theory: Advances and Applications
Volume	221
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Other

Other	21st International Workshop on Operator Theory and Applications, 2010
Country/Territory	Germany
City	Berlin
Period	10/7/12 → 10/7/16

Keywords

2-dimensional exterior domain
Global in time unique existence theorem
L-L decay estimate
Local energy decay

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/978-3-0348-0297-0_17

Cite this

Enomoto, Y., & Shibata, Y. (2012). About compressible viscous fluid flow in a 2-dimensional exterior domain. In W. Arendt, J. Behrndt, V. Mehrmann, K-H. Förster, J. A. Ball, & C. Trunk (Eds.), Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 2010 (pp. 305-321). (Operator Theory: Advances and Applications; Vol. 221). Springer International Publishing. https://doi.org/10.1007/978-3-0348-0297-0_17

About compressible viscous fluid flow in a 2-dimensional exterior domain. / Enomoto, Yuko; Shibata, Yoshihiro.
Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 2010. ed. / Wolfgang Arendt; Jussi Behrndt; Volker Mehrmann; Karl-Heinz Förster; Joseph A. Ball; Carsten Trunk. Springer International Publishing, 2012. p. 305-321 (Operator Theory: Advances and Applications; Vol. 221).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Enomoto, Y & Shibata, Y 2012, About compressible viscous fluid flow in a 2-dimensional exterior domain. in W Arendt, J Behrndt, V Mehrmann, K-H Förster, JA Ball & C Trunk (eds), Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 2010. Operator Theory: Advances and Applications, vol. 221, Springer International Publishing, pp. 305-321, 21st International Workshop on Operator Theory and Applications, 2010, Berlin, Germany, 10/7/12. https://doi.org/10.1007/978-3-0348-0297-0_17

Enomoto Y, Shibata Y. About compressible viscous fluid flow in a 2-dimensional exterior domain. In Arendt W, Behrndt J, Mehrmann V, Förster K-H, Ball JA, Trunk C, editors, Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 2010. Springer International Publishing. 2012. p. 305-321. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-0348-0297-0_17

Enomoto, Yuko ; Shibata, Yoshihiro. / About compressible viscous fluid flow in a 2-dimensional exterior domain. Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 2010. editor / Wolfgang Arendt ; Jussi Behrndt ; Volker Mehrmann ; Karl-Heinz Förster ; Joseph A. Ball ; Carsten Trunk. Springer International Publishing, 2012. pp. 305-321 (Operator Theory: Advances and Applications).

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AB - 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. We 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].

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About compressible viscous fluid flow in a 2-dimensional exterior domain

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