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Applications of degenerate bifurcation equations to the taylor problem and the water wave problem

  • Stability, Bifurcation, Attractors And Related Problems
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The Navier-Stokes Equations Theory and Numerical Methods

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References

  1. H. Fujii, M. Mimura and Y. Nishiura, A picture of the global bifurcation diagram in ecological interacting and diffusing systems, Physica 5D (1982), 1–42.

    MathSciNet  Google Scholar 

  2. H. Fujii, Y. Nishiura and Y. Hosono, On the structure of multiple existence of stable stationary solutions in systems of reaction-diffusion equations, Patterns and Waves-Qualitative analysis of nonlinear differential equations, eds. T. Nishida, M. Mimura and H. Fujii, North-Holland (1986), 157–219.

    Google Scholar 

  3. M. Golubitsky and D. Schaeffer, Imperfect bifurcation in the presence of symmetry, Comm. Math. Phys. 67 (1979), 205–232.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Golubitsky and D. Schaeffer, “Singularities and Groups in bifurcation theory, vol 1,” Springer Verlag, New York, 1985.

    Book  MATH  Google Scholar 

  5. M. Golubitsky, I. Stewart and D. Schaeffer, “Singularities and Groups in bifurcation theory, vol 2,” Springer Verlag, New York, 1988.

    Book  MATH  Google Scholar 

  6. H. Okamoto, O(2)-equivariant bifurcation equations with mode (1,2), Sci. Papers College of Arts and Sci., Univ. of Tokyo 39 (1989), 1–43.

    MathSciNet  MATH  Google Scholar 

  7. H. Okamoto and S.J. Tavener, Degenerate O(2)-equivariant bifurcation equations and their application to the Taylor problem, preprint.

    Google Scholar 

  8. H. Okamoto, On the problem of water waves of permanent configuration, Nonlinear Anal. Theory and Appl. (in press).

    Google Scholar 

  9. S.J. Tavener and K.A. Cliffe, Primary flow exchange mechanisms in the Taylor apparatus applying impermeable stress-free boundary conditions.

    Google Scholar 

  10. R. Temam, “Navier-Stokes Equations,” North-Holland, Amsterdam, New York, Oxford, 1984.

    MATH  Google Scholar 

  11. M. Shōji, New bifurcation diagrams in the problem of permanent progressive waves, J. Fac. Sci., Univ. Tokyo, Sec. IA 36 (1989), 571–613.

    MathSciNet  MATH  Google Scholar 

  12. H. Okamoto and M. Shōji, Normal forms of the bifurcation equations in the problem of capillary-gravity waves, preprint.

    Google Scholar 

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John G. Heywood Kyûya Masuda Reimund Rautmann Vsevolod A. Solonnikov

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© 1990 Springer-Verlag

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Okamoto, H. (1990). Applications of degenerate bifurcation equations to the taylor problem and the water wave problem. In: Heywood, J.G., Masuda, K., Rautmann, R., Solonnikov, V.A. (eds) The Navier-Stokes Equations Theory and Numerical Methods. Lecture Notes in Mathematics, vol 1431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086062

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  • DOI: https://doi.org/10.1007/BFb0086062

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52770-1

  • Online ISBN: 978-3-540-47141-7

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