Gordevskyy, V. D. Transitional regime between vortical states of a gas. (English) Zbl 1021.76045 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 53, No. 3-4, 481-494 (2003). 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. Cited in 2 Documents 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 Keywords:Boltzmann equation; vortical flows; gas of hard spheres; vortical states; transitional regime; bimodal distribution; uniform integral residual PDF BibTeX XML Cite \textit{V. D. Gordevskyy}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 53, No. 3--4, 481--494 (2003; Zbl 1021.76045) Full Text: DOI References: [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.