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Some solutions of continuum equations for an incompressible viscous medium

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Abstract

We consider the Navier-Stokes equations for an incompressible medium that fills at any time t ≥ 0 an open axially symmetric cylindric layer D. We find solutions of these equations in the class of motions described by velocity fields whose lines for t ≥ 0 coincide with their vortex lines and lie on axially symmetric cylindrical surfaces in D.

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References

  1. N. I. Chernykh, Yu. N. Subbotin, and V. P. Vereshchagin, “Transformation that changes the geometric structure of a vector field,” Proc. Steklov Inst. Math., Suppl. 2, S118–S128 (2009).

    Google Scholar 

  2. I. S. Gromeka, “Some cases of motion of an incompressible fluid: Doctoral Dissertation in Physics and Mathematics (Kazan, 1994),” in Collection of Works (Izd. Akad. Nauk SSSR, Moscow, 1952) [in Russian].

    Google Scholar 

  3. V. P. Vereshchagin, Yu. N. Subbotin, and N. I. Chernykh, “On the mechanics of helical flows in an ideal incompressible nonviscous continuous medium,” Proc. Steklov Inst. Math. 284(Suppl. 1), S159–S174 (2014).

    Article  Google Scholar 

  4. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York 1961; Nauka, Moscow, 1977).

    MATH  Google Scholar 

  5. M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1958) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Russian State Professional-Pedagogical University, ul. Mashinostroitelei 11, Yekaterinburg, 620012, Russia

    V. P. Vereshchagin

  2. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    Yu. N. Subbotin & N. I. Chernykh

  3. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russia

    Yu. N. Subbotin & N. I. Chernykh

Authors
  1. V. P. Vereshchagin
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  2. Yu. N. Subbotin
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  3. N. I. Chernykh
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Additional information

Original Russian Text © V.P. Vereshchagin, Yu.N. Subbotin, N.I. Chernykh,, 2013, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Vol. 19, No. 4.

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Vereshchagin, V.P., Subbotin, Y.N. & Chernykh, N.I. Some solutions of continuum equations for an incompressible viscous medium. Proc. Steklov Inst. Math. 287 (Suppl 1), 208–223 (2014). https://doi.org/10.1134/S008154381409020X

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  • DOI: https://doi.org/10.1134/S008154381409020X

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