zbMATH — the first resource for mathematics

Transitional regime between vortical states of a gas. (English) Zbl 1021.76045
Summary: The process of interaction between two vortical flows in a gas of hard spheres is approximately described by the bimodal distribution of a special form. Both the flows rotate about the axes which can move with arbitrary linear velocities. Some sufficient conditions for the infinitesimality of a uniform integral residual between the sides of Boltzmann equation are obtained.

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76U05 General theory of rotating fluids
35Q35 PDEs in connection with fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
Full Text: DOI
[1] Cercignani, C., The Boltzmann equation and its applications, (1988), Springer New York · Zbl 0646.76001
[2] T. Carleman, Problemes matematiques dans la theorie cinetique des gas, Almqvist & Wiksells, Uppsala, 1957. · Zbl 0077.23401
[3] Bobylev, A.V., On the exact solutions of the Boltzmann equation, Dokl. akad. sci. of USSR, 225, 6, 1296-1299, (1975)
[4] Ernst, H.M., Exact solutions of the nonlinear Boltzmann equation, J. statist. phys., 34, 5/6, 1001-1017, (1984) · Zbl 0595.76076
[5] Petrina, D.Ya.; Mishchenko, A.V., On the exact solutions of the one class of the Boltzmann equations, Dokl. akad. sci. of USSR, 298, 2, 338-342, (1988) · Zbl 0659.76087
[6] Gordevsky, V.D., Approximate bimodal solutions of the Boltzmann equation for hard spheres, Math. phys. anal. geom., 2, 2, 168-176, (1995) · Zbl 0842.76073
[7] Gordevsky, V.D., A criterium of smallest of the difference for bimodal solution of the Boltzmann equation, Math. phys. anal. geom., 4, 1/2, 46-58, (1997)
[8] Gordevskii, V.D., An approximate biflow solution of the Boltzmann equation, Theoret. math. phys., 114, 1, 126-136, (1998)
[9] Gordevsky, V.D., Trimodal approximate solutions of the non-linear Boltzmann equation, Math. meth. appl. sci., 21, 1479-1494, (1998) · Zbl 0915.76076
[10] Gordevskyy, V.D., Biflow distribution with screw modes, Theoret. math. phys., 126, 2, 234-249, (2001) · Zbl 0997.35055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.