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Vanishing viscosity limit for a smoke ring with concentrated vorticity

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Abstract

We study the vanishing viscosity limit for an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated.

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References

  1. Ambrosetti A., Struwe M.: Existence of steady rings in an ideal fluid. Arch. Ration. Mech. Anal. 108, 97–108 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Batchelor K.G.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (1967)

    MATH  Google Scholar 

  3. Benedetto D., Caglioti E., Marchioro C.: On the motion of a vortex ring with sharply concentrated vorticity. Math. Methods Appl. Sci. 23, 147–169 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Fraenkel L.E., Berger M.S.: A global theory of steady vortex rings in an ideal fluid. Acta Math. 132, 13–51 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gallay, Th.: Interaction of vortices in viscous planar flows (2009, preprint)

  6. Ladyzhenskaya O.A.: Unique solvability in large of a three-dimensional Cauchy problem for the Navier–Stokes equations in the presence of axial symmetry. Zapisky Nauchnych Sem. LOMI 7, 155–177 (1968)

    MATH  Google Scholar 

  7. Marchioro C.: On the vanishing viscosity limit for two-dimensional Navier–Stokes equations with singular initial data. Math. Methods Appl. Sci. 12, 463–470 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Marchioro C.: On the inviscid limit for a fluid with a concentrated vorticity. Commun. Math. Phys. 196, 53–65 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Marchioro C.: Vanishing viscosity limit for an incompressible fluid with concentrated vorticity. J. Math. Phys. 48(065302), 1–16 (2007)

    MathSciNet  Google Scholar 

  10. Marchioro C., Negrini P.: On a dynamical system related to fluid mechanics. Nonlinear Differ. Equ. Appl. 6, 473–499 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Marchioro C., Pulvirenti M.: Mathematical theory of incompressible nonviscous fluids. In: Applied Mathematical Sciences, vol. 96. Springer, New York (1994)

    Book  Google Scholar 

  12. Newton P.K.: The N-vortex problem, analytical techniques. In: Applied Mathematical Sciences, vol. 145. Springer, New York (2001)

    Google Scholar 

  13. Shariff K., Leonard A.: Vortex rings. Ann. Rev. Fluid Mech. 24, 235–279 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  14. Turkington B.: On the evolution of a concentrated vortex in an ideal fluid. Arch. Ration. Mech. Anal. 97, 75–87 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ukhovskii M., Yudovitch V.: Axially symmetric flows of ideal and viscous fluids filling the whole space. J. Appl. Math. Mech. 32, 52–69 (1968)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Sapienza Università di Roma, P.le Aldo Moro 2, 00185, Rome, Italy

    Enrico Brunelli & Carlo Marchioro

Authors
  1. Enrico Brunelli
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  2. Carlo Marchioro
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Correspondence to Enrico Brunelli.

Additional information

Communicated by D. Chae

Work performed under the auspices of GNFM-INDAM and the Italian Ministry of the University (MIUR).

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Brunelli, E., Marchioro, C. Vanishing viscosity limit for a smoke ring with concentrated vorticity. J. Math. Fluid Mech. 13, 421–428 (2011). https://doi.org/10.1007/s00021-010-0024-z

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  • DOI: https://doi.org/10.1007/s00021-010-0024-z

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