Solution of the Ovsyannikov Problem of Two-Dimensional Isothermal Motion of a Polytropic Gas
- 19 Downloads
We study an overdetermined system of partial differential equations which describes the two-dimensional isothermal motion of a polytropic gas. The system is reduced to a passive form and is completely integrated. The resulting solutions are treated as ideal incompressible fluid flows bounded by a free surface or a moving solid wall.
Keywordsisothermal gas flows thermal motion of gas free-boundary ideal flow overdetermined systems exact solutions
Unable to display preview. Download preview PDF.
- 5.Yu. V. Shan’ko, “On an Overdetermined System of Equations of Motion of a Continuous Medium,” in Reshetnev Readings, Proc. of the 17th Int. Sci. Conf., Krasnoyarsk, November 12–14, 2013 (Sib. Gos. Aerokosm. Univ., Krasnoyarsk, 2013), Part 2, pp. 122–123.Google Scholar
- 6.S. V. Khabirov, “General Solution of a Planar Hydrodynamic Model of Motion with a One-Parameter Thermodynamic System and Variable Entropy,” in New Mathematical Models of Continuum Mechanics: Construction and Investigation, Abstracts of the All Russian Conf. Novosibirsk, April 18–22, 2014 (Lavrentyev Institute of Hydrodynamics, Sib. Branch, Russian Acad. of Sci., Novosibirsk, 2014), pp. 140–141.Google Scholar
- 8.A. C. Hearn and R. Schopf, REDUCE User’s Manual; http://reduce-algebra.sourceforge.net/manual/manual.html.Google Scholar
- 10.P. K. Rashevskii, Course in Differential Geometry (Gostekhteoretizdat, Moscow–Leningrad, 1950) [in Russian].Google Scholar
- 11.A. A. Abrashkin and E. I. Yakubovich, Vortex Dynamics in Lagrangian Description (Fizmatlit, Moscow, 2006) [in Russian].Google Scholar
- 12.V. I. Nalimov and V. V. Pukhnachov, Unsteady Motion of an Ideal Fluid with a Free Boundary (Novosib. Gos. Univ., Novosibirsk, 1975) [in Russian].Google Scholar
- 13.Yu. V. Shan’ko, “Analysis of Overdetermined System that Describes the Special Class of Two-Dimensional Motion of an Ideal Fluid,” http://arxiv.org/abs/1608.08186.Google Scholar