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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.

MSC:
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
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[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
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