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Boundary layer equations in the problem of axially symmetric jet flow

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The problem of stationary axially symmetric jet flour of a viscous incompressible fluid from a round tube into a free space is considered. The mathematical model of this flow in the Mises variables and for large Reynolds numbers is reduced to the boundary-value problem for a degenerate integro-differential equation of the second order. The existence and uniqueness of bounded solutions to this problem are proved, and stabilization as a time-like variable increases is shown. Bibliography: 7 titles.

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References

  1. V. V. Puchnachev, Motion of Viscous Fluid with Free Boundaries [in Russian], Novosib. State Univ. (1989).

  2. V. A. Solonnikov, “Probleme de frontiere libre a la sortie d’une tube cylindrique,” Asympt. Anal., 17, 135–163 (1998).

    MATH  MathSciNet  Google Scholar 

  3. V. A. Solonnikov, “Stationary free boundary problems for the Navier–Stokes equations,” Pitman Research Notes, 392, 147–192 (1998).

    MathSciNet  Google Scholar 

  4. R. Mises, “Bemerkungen zur Hydrodynamik,” ZAMM, 7, 425431 (1927).

    Google Scholar 

  5. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Society, Providence, Rhode Island (1968).

    Google Scholar 

  6. V. S. Belonosov, “Estimates of solutions of parabolic equations in Hölder weight classes and some of their applications,” Mat. Sb., 110, 163–188 (1979).

    MathSciNet  Google Scholar 

  7. T. I. Zelenyak, “Stabilization of solutions of boundary–value problems for parabolic equations of the second order with one spatial variable,” Diff Uravn., IV, 34–45 (1968).

    Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mechanics SibD RAS, Novosibirsk, Russia

    V. S. Belonosov

  2. Lavrentiev Institute of Hydrodynamics SibD RAS, Novosibirsk, Russia

    V. V. Pukhnachev

Authors
  1. V. S. Belonosov
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  2. V. V. Pukhnachev
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Corresponding author

Correspondence to V. S. Belonosov.

Additional information

To Vsevolod Alekseevich Solonnikov on the occasion of his 75th birthday

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 362, 2008, pp. 48-63.

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Belonosov, V.S., Pukhnachev, V.V. Boundary layer equations in the problem of axially symmetric jet flow. J Math Sci 159, 411–419 (2009). https://doi.org/10.1007/s10958-009-9453-8

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  • DOI: https://doi.org/10.1007/s10958-009-9453-8

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