Continual distribution with screw modes
AbstractExplicit 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.
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.
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