Skip to main content
SpringerLink
Log in
Book cover

Advances in Mathematical Fluid Mechanics pp 513–551Cite as

On a C 0 Semigroup Associated with a Modified Oseen Equation with Rotating Effect

  • Chapter
  • First Online:

Abstract

In this paper, we show the unique existence of solutions to the nonstationary problem for the modified Oseen equation with rotating effect in Ω

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. E. Bogovskiǐ, Solution of Some Vector Analysis Problems connected with Operators div and grad (Russian). Trudy Seminar S.L. Sobolev, No. 1, 80, Akademia Nauk SSR, Sibirskoe Otdelenie Matematiki, Nowosibirsk, 5–40 (1980)

    Google Scholar 

  2. Y. Enomoto and Y. Shibata, On the rate of decay of the Oseen semigroup in exterior domains and its application to Navier-Stokes equation. J. Math. Fluid Mech. 7, 339–367 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. R. Farwig, An L q-analysis of viscous fluid flow past a rotating obstacle. Tôhoku Math. J. 58, 129–147 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Farwig, T. Hishida and D. Müller, L q-theory of a singular “winding” integral operator arising from fluid dynamics. Pacific. J. Math. 215, 297–312 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Farwig and J. Neustupa, On the Spectrum of an Oseen-type operator arising from flow past a rotating body. Integr. Equat. Operat. Theor. 62, 169–189 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Farwig and H. Sohr, Generalized resolvent estimates for the Stokes operator in bounded and unbounded domains. J. Math. Soc. Japan 46, 607–643 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Fujiwara and H. Morimoto, An L r -theory of the Helmholtz decomposition of vector fields. J. Fac. Sci. Univ. Tokyo, Sect. Math. 24, 685–700 (1977)

    MATH  MathSciNet  Google Scholar 

  8. G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol. I: Linear Steady Problems, Vol. II: Nonlinear Steady Problems. Springer Tracts in Nat. Ph. 38, 39, Springer Verlag, New York (1994) 2nd edition (1998)

    Google Scholar 

  9. G. P. Galdi and A. L. Silvestre, The steady motion of a Navier-Stokes liquid around a rigid body. Arch. Rational Mech. Anal. 184, 371–400 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  10. G. P. Galdi and A. L. Silvestre, Further results on steady-state flow of a Navier-Stokes liquid around a rigid body, Existence of the wake. Kyoto Conference on the Navier-Stokes Equations and their applications, RIMS Kokyuroku Bessatsu B1, 127–143 (2007)

    Google Scholar 

  11. M. Geissert, H. Heck and M. Hieber, L p-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle. J. Reine Angew. Math. 596, 45–62 (2006)

    MATH  MathSciNet  Google Scholar 

  12. M. Geissert, H. Heck and M. Hieber, On the equation div u = g and Bogovskii’s operator in Sobolev spaces of negative order. Operat. Theor. Advan. Appl. 168, 113–121 (2006)

    Article  MathSciNet  Google Scholar 

  13. T. Hishida and Y. Shibata, L p –L q estimate of the Stokes operator and Navier-Stokes flows in the exterior of a rotating obstacle. Arch. Rational Mech. Anal. 193, 339–421 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. T. Kobayashi and Y. Shibata, On the Oseen equation in the three dimensional exterior domains. Math. Ann. 310, 1–45 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  15. T. Miyakawa, On non-stationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J. 12, 115–140 (1982)

    MATH  MathSciNet  Google Scholar 

  16. A. Noll and J. Saal, H ∞-calculus for the Stokes operator on L q -spaces. Math. Z. 244, 651–688 (2003)

    MATH  MathSciNet  Google Scholar 

  17. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Appl. Math. Sci. Springer-Verlag, New York, 44 (1983)

    Google Scholar 

  18. Y. Shibata, On the exterior initial boundary value problem for Navier-Stokes equations. Quartely Appl. Math. LVII(1), 117–155 (1999)

    MathSciNet  Google Scholar 

  19. Y. Shibata, Time-global solutions of nonlinear evolution equations and their stability. Amer. Math. Soc. Transl. 211(2), 87–105 (2003)

    MathSciNet  Google Scholar 

  20. Y. Shibata, On the Oseen semigroup with rotating effect. Functional Analysis and Evolution Equations, The Günter Lumer Volume, H. Amann et al (eds.), Birkhauser Verlag, Basel, 595–611 (2008)

    Chapter  Google Scholar 

  21. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators. North Holland, Amsterdam (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Research Institute of Science and Engineering, Waseda University, 169-8555, Tokyo, Japan

    Yoshihiro Shibata

Authors
  1. Yoshihiro Shibata
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoshihiro Shibata .

Editor information

Editors and Affiliations

  1. Interdisziplinäres Zentrum für, Universität Heidelberg, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Rolf Rannacher

  2. Depto. Mathemática, Istituto Superior Técnico, Av. Rovisco Pais, Lisboa, 1049-001, Portugal

    Adélia Sequeira

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Shibata, Y. (2010). On a C 0 Semigroup Associated with a Modified Oseen Equation with Rotating Effect. In: Rannacher, R., Sequeira, A. (eds) Advances in Mathematical Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04068-9_29

Download citation

Publish with us

Policies and ethics

Search

Navigation