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A singular perturbation problem arising in Oseen’s spiral flows

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Abstract

Oseen’s spiral flows for viscous incompressible fluid are considered. Their limiting behavior as the Reynolds number tends to infinity is rigorously analyzed and the width of the interior layer is proved to be of O(R−1/2), whereR is the Reynolds number.

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References

  1. M. Abramowitz and I.A. Stegun (eds.), Handbook of Mathematical Functions. Dover, 1970.

  2. R. Berker, Intégration des équations du mouvement d’un fluide visqueux incompressible. Handbuch der Physik (Vol.VIII/2), 1963, 1–384.

  3. H. Ikeda, Stability characteristics of transition layer solutions. J. Dynam. Diff. Eqns.,5 (1993), 625–671.

    Article  MATH  Google Scholar 

  4. D.F. Lawden, Elliptic Functions and Applications. Springer-Verlag, 1989.

  5. H. Okamoto, Localization of singularities in inviscid limit — numerical examples. Proceedings of Navier-Stokes Equations: Theory and Numerical Methods (ed. R. Salvi), Longman, Pitman Research Notes in Mathematics Series388, 1998, 220–236.

  6. C.W. Oseen, Exacte Lösungen der hydrodynamischen Differentialgleichungen. I. Ark. Mat. Astronom. Fysik,20, No. 14 (1928), 1–24; II. (ibid), No.22 (1928), 1–9.

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  7. E.T. Whittaker and G.N. Watson, A Course of Modern Analysis (Fourth Ed.). Cambridge Univ. Press, 1927.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Toyama University, 930-8555, Toyama, Japan

    H. Ikeda

  2. Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, 739-8526, Higashi-Hiroshima, Japan

    M. Mimura

  3. Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan

    H. Okamoto

Authors
  1. H. Ikeda
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  2. M. Mimura
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  3. H. Okamoto
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Additional information

Partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan, #11640107.

Partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan, #11214101.

Partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan, #11304005.

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Ikeda, H., Mimura, M. & Okamoto, H. A singular perturbation problem arising in Oseen’s spiral flows. Japan J. Indust. Appl. Math. 18, 393–403 (2001). https://doi.org/10.1007/BF03168582

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  • DOI: https://doi.org/10.1007/BF03168582

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