The interaction of the asymmetrical screw flows for the BryanPidduck model 

Author 
gordevskyy2006@gmail.com^{1}, hukalov@ilt.kharkov.ua^{2}
1) V.N. Karazin Kharkiv National University
Kharkiv, Ukraine; 2) B.Verkin Institute for Low Temperature Physics
and Engineering, Kharkiv, Ukraine

Abstract 
Some approximate solutions of the Boltzmann equation for a model of rough spheres are
constructed. Several sufficient conditions which minimize the uniformintegral error between
parts of the BryanPidduck equation are obtained.

Keywords 
the BryanPidduck equation; bimodal distribution; uniformintegral error

DOI 
doi:10.15330/ms.50.2.173188

Reference 
1. S. Chapman, T.G. Cowling, The mathematical theory of nonuniform gases, Cambridge Univ. Press,
Cambridge, 1952.
2. G.H. Bryan, On the application of the determinantal relation to the kinetic theory of polyatomic gases, Rept. Brit. Assoc. Adv. Sci., 64 (1894), 102–106. 3. F.B. Pidduck, The kinetic theory of a special type of rigid molecule, Proc. Roy. Soc., A101 (1922), 101–110. 4. C. Cercignani, M. Lampis, On the kinetic theory of a dense gas of rough spheres, J. Statist. Phys., 53 (1988), 655–672. 5. V.D. Gordevskyy, Explicit approximate solutions of the Boltzmann equation for the model of rough spheres, Reports of the National Academy of Sciences of Ukraine, 4 (2000), 10–13. (in Ukrainian) 6. V.D. Gordevskyy, Approximate billow solutions of the kinetic BryanPidduck equation, Math. Meth. Appl. Sci., 23 (2000), 1121–1137. 7. V.D. Gordevskii, A.A. Gukalov Interaction of locally Maxwellian flows in the model of rough spheres, Theor. Math. Phys, 176 (2013), ¹2, 322–336. (in Russian) 8. V.D. Gordevskyy, A.A. Gukalov, Interaction of the eddy flows in the Bryan–Pidduck model, Vysnik Kharkiv Univ., Ser. Mat. Prykl. Mat. Mech., 64 (2011), ¹2, 27–41. (in Russian) 9. V.D. Gordevskyy, A.A. Gukalov, Maxwell distributions in a model of rough spheres, Ukr. Mat. Zh., 63 (2011), ¹5, 629–639. (in Russian) 10. V.D. Gordevskyy, E.S. Sazonova Asymmetrical bimodal distributions with screw modes, Math. Phys., Anal., Geom., 3 (2011), V.7, 212–224. 11. C. Cercignani, Theory and Application of the Boltzmann Equation, Elsevier, New York, 1975. 
Pages 
173188

Volume 
50

Issue 
2

Year 
2018

Journal 
Matematychni Studii

Full text of paper  
Table of content of issue 