Continual distribution with screw modes

  • В. Д. Гордевский V.N.Karazin Kharkiv National University
  • О. С. Сазонова V.N.Karazin Kharkiv National University
DOI: https://doi.org/10.26565/2221-5646-2016-84-08
Keywords: hard spheres, Boltzmann equation, Maxwellian, screws, uniformintegral remainder, continual distribution

Abstract

Explicit approximate solution of the Boltzmann equation for the hardsphere model are built. It has the kind of continual distribution in the case of local Maxwellians of special form describing the screw-shaped stationary equilibrium states of a gas. Some limited cases, in which this distribution minimized the uniform-integral remainder between the sides of this equation are obtained.

Downloads

Download data is not yet available.

References

Cercignani C. Theory and Application of the Boltzmann Equation. – Scottish Academic Press, Edinburgh, 1975.

Kogan M. Dynamics of Diluted Gas. – Nauka, Moscow, 1967. (in Russian).

Carleman T. Problems Mathematiques dans la Theorie Cinetique des Gas. – Almqvist Wiksells, Uppsala, 1957.

Bobylev A.V. Exact solutions of the Boltzmann equation. // Sov. Phys. Dokl., 1976. – 20. – P. 822–824

Krook K.,Wu T.T. Exact solutions of the Boltzmann equation // Phys. Fluids, 1977. – V. 20, 10(1). – P. 1589–1595.

Ernst H.M. Exact solutions of the nonlinear Boltzmann equation // J. Statist. Phys., 1984. – V. 34, 5/6. – P. 1001–1017.

Gordevskyy V.D. Biflow Distributions with Screw Modes // Theor. Math. Phys., 2001. – V. 126, 2. – P. 234–249.

Gordevskyy V.D. Rotating Flows with Acceleration and Compacting in the Model of Hard Spheres // Theor. Math. Phys., 2009. – V. 161, 2. – P. 1558–1566.

Gordevskyy V.D. Transitional regime between vortical states of a gas // Nonl. Analysis (NA 3752), 2003. – V. 53, 3-4. – P. 481–494.

Gordevskyy V.D. Vorticies in a gas of hard spheres // Theor. Math. Phys., 2003. – V. 135, 2. – P. 704–713.

Gordevskyy V.D. Trimodal Approximate Solutions of the Non-linear Boltzmann Equation // Math. Meth. Appl. Sci., 1998. – 21. – P. 1479–1494.

Gordevskyy V.D., Sazonova E.S. Continuum analogue of bimodal distribution // Theor. Math. Phys., 2012. – V. 171, 3. – P. 839–847

Gordevskyy V.D. An approximate two-flow solution to the Boltzmann equation // Theor. Math. Phys., 1998. – V. 114, 1. – P. 99–108.

Gordevskyy V. D., Sazonova E. S. Asymmetrical bimodal distributions with screw modes // Math. Phys., Anal., Geom., 2011. – V. 7, 3. – P. 212–224.
Published
2016-12-15
Cited
How to Cite
Гордевский, В. Д., & Сазонова, О. С. (2016). Continual distribution with screw modes. Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, 84, 112-122. https://doi.org/10.26565/2221-5646-2016-84-08
Issue
Vol. 84 (2016)
Section
Статті

The copyright holder is the author.

Authors who publish with this journal agree to the following terms:

1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal. (Attribution-Noncommercial-No Derivative Works licence).

2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (see The Effect of Open Access).