Abstract:
Generalized characteristics and Riemann invariants that are preserved along the characteristics are found for a kinetic model of motion of bubbles in a fluid. Conditions that ensure the hyperbolicity of a set of equations of a bubbly flow are obtained. It is shown that the set of equations of motion has an infinite number of conservation laws. An infinite series of generalized symmetries admitted by the equations is constructed. Solutions that are invariant under the generalized symmetries of solution and describe the propagation of running and simple waves in a bubbly fluid are found.
Citation:
V. M. Teshukov, “Characteristics, conservation laws, and symmetries of the kinetic equations of motion of bubbes in a fluid”, Prikl. Mekh. Tekh. Fiz., 40:2 (1999), 86–100; J. Appl. Mech. Tech. Phys., 40:2 (1999), 263–275
\Bibitem{Tes99}
\by V.~M.~Teshukov
\paper Characteristics, conservation laws, and symmetries of the kinetic equations of motion of bubbes in a fluid
\jour Prikl. Mekh. Tekh. Fiz.
\yr 1999
\vol 40
\issue 2
\pages 86--100
\mathnet{http://mi.mathnet.ru/pmtf3058}
\elib{https://elibrary.ru/item.asp?id=35309407 }
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 1999
\vol 40
\issue 2
\pages 263--275
\crossref{https://doi.org/10.1007/BF02468523}
Linking options:
https://www.mathnet.ru/eng/pmtf3058
https://www.mathnet.ru/eng/pmtf/v40/i2/p86
This publication is cited in the following 8 articles:
Zakhar V. Makridin, Maxim V. Pavlov, “Multi‐dimensional conservation laws and integrable systems”, Stud Appl Math, 143:4 (2019), 339
Alexander A. Chesnokov, Maxim V. Pavlov, “The Russo–Smereka kinetic equation: Conservation laws, reductions and numerical solutions”, Physica D: Nonlinear Phenomena, 303 (2015), 50
A. K. Khe, A. A. Chesnokov, “Propagation of nonlinear perturbations in a quasineutral collisionless plasma”, J. Appl. Mech. Tech. Phys., 52:5 (2011), 677–688
E. V. Ferapontov, D. G. Marshall, “Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor”, Math. Ann., 339:1 (2007), 61
Maxim V. Pavlov, “Hydrodynamic chains and the classification of their Poisson brackets”, Journal of Mathematical Physics, 47:12 (2006)
G. Russo, V. M. Teshukov, A. A. Chesnokov, “Special class of solutions of the kinetic equation of a bubbly fluid”, J. Appl. Mech. Tech. Phys., 46:2 (2005), 176–184
G. Russo, V. M. Teshukov, A. A. Chesnokov, “Special class of solutions of the kinetic equation of a bubbly fluid”, J Appl Mech Tech Phys, 46:2 (2005), 176
G. Russo, V. M. Teshukov, A. A. Chesnokov, “Special class of solutions of the kinetic equation of a bubbly fluid”, J Appl Mech Tech Phys, 46:2 (2005), 176
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