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Some Problems in Vortex Theory

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Statistical Physics and Dynamical Systems

Part of the book series: Progress in Physics ((PMP,volume 10))

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Abstract

In this lecture we want to study the following Hamiltonian dynamical system. called “vortex system”

(1.1)

and where H has the form

(1.2)

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References

  1. H. Helmholtz. Phil. Mag., 32. p. 485 (1867)

    Google Scholar 

  2. G. Kirchhoff. Vorlesungen ueber Math. Phys. Teubener Leipzig (1883)

    Google Scholar 

  3. H. Poincare. Theories des Turbillons. George Carre (1983)

    Google Scholar 

  4. Lord Kelvin. Mathematical and Physical Papers. Vol IV (No. 10, 12) Cambridge Univ. Press p. 563

    Google Scholar 

  5. C. C. Lin. On the motion of Vortices vin Two Dimension. Toronto University Press p. 39

    Google Scholar 

  6. C. Marchioro, M. Pulvirenti. Commun. Math. Phys., 91, 563 (1983)

    Article  Google Scholar 

  7. B. Turkington. On the evolution of a concentrated vortex in a ideal fluid (preprint 1984)

    Google Scholar 

  8. C. Marchioro, E. Pagani. Euler evolution of two concentrated vortices moving in a bidimensional bounded region. (in preparation).

    Google Scholar 

  9. H. Aref. Physics of Fluid. 22, 393 (1979)

    Article  Google Scholar 

  10. D. Dürr, M. Pulvirenti, Commun. Math. Phys. 85. 265 (1982)

    Article  Google Scholar 

  11. C. Marchioro, M. Pulvirenti. Lecture Notes in Phys. 203. Springer-Verlag (1984)

    Google Scholar 

  12. H. Aref. Ann. Rev. Fluid Mech., 15 (1983)

    Google Scholar 

  13. K. M. Khanin, Physica D 4. 261 (1982)

    Article  Google Scholar 

  14. A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 98, 527 (1954)

    Google Scholar 

  15. V. l. Arnold. Usp. Mat. Nauk. 18. 13 (1963)

    Google Scholar 

  16. J. Moser. Math. Ann., 169. 136 (1967)

    Article  Google Scholar 

  17. L. Onsager. Suppl. Nuovo Cimento. 6. “79 (1949)

    Google Scholar 

  18. J. Fröhlich. D. Ruelle. Commun. Math. Phys., 7, 1 (1982)

    Article  Google Scholar 

  19. R. H. Kraichnan. D. Montgomery. Rep. Prog. Phys., 4, 547 (1980)

    Article  Google Scholar 

  20. O. Haid. V. Mauceri Del Prete. Math. Comp. 32. 791 (1978)

    Google Scholar 

  21. O. Haid. SIAM J. Numer. Anal., 16, 726 (1979)

    Article  Google Scholar 

  22. C. Marchioro, M. Pulvirenti. Commun. Math. Phys., 84, 483 (1982)

    Article  Google Scholar 

  23. J. T. Beale, A. Majda. Math. Comp., 39, 1 (1982), 39, 29 ( 1982

    Google Scholar 

  24. W. Braun, K. Hepp. Commun. Math. Phys., 56, 101 (1977)

    Article  Google Scholar 

  25. R. L. Dobrushin. Sov. J. Funct. Anal. 13, 115 (1979)

    Article  Google Scholar 

  26. H. Neunzert. Lect. Notes in Math. 1048 (1984)

    Google Scholar 

  27. A. J. Chorin. J. Fluid Mech., 57, 785 (1973)

    Article  Google Scholar 

  28. G. Benfatto, M. Pulvirenti. Generation of vorticity near the boundary in two dimensional flows (Comm. Math. Phys 1984 )

    Google Scholar 

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Authors
  1. C. Marchioro
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Editor information

Editors and Affiliations

  1. MTA MKI, Realtanoda u. 13-15, H-1053, Budapest, Hungary

    J. Fritz  & D. Szász  & 

  2. Dept. of Physics, Lyman Laboratory, Harvard University, 02138, Cambridge, MA, USA

    A. Jaffe

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© 1985 Springer Science+Business Media New York

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Marchioro, C. (1985). Some Problems in Vortex Theory. In: Fritz, J., Jaffe, A., Szász, D. (eds) Statistical Physics and Dynamical Systems. Progress in Physics, vol 10. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6653-7_18

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  • DOI: https://doi.org/10.1007/978-1-4899-6653-7_18

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4899-6655-1

  • Online ISBN: 978-1-4899-6653-7

  • eBook Packages: Springer Book Archive

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