Abstract:
The equations of ideal hydrodynamics are considered with the state equation in the form of the pressure represented as the sum of density and entropy functions. Some twelve-dimensional Lie algebra corresponds to the admissible group of transformations. Basing on the two-dimensional subalgebras of the Lie algebra, we construct the rank 2 invariant submodels of canonical form and evolutionary type. The form is refined of the rank 2 invariant submodels of canonical form and evolutionary type for the eleven-dimensional Lie algebra admitted by the gas dynamics equations with the state equation of the general type.
Keywords:
equations of ideal hydrodynamics, state equation, admissible subalgebra, representation of invariant solution, invariant submodel, submodel of evolutionary type, canonical form of a submodel.
Citation:
D. T. Siraeva, “The canonical form of the rank 2 invariant submodels of evolutionary type in ideal hydrodynamics”, Sib. Zh. Ind. Mat., 22:2 (2019), 70–80; J. Appl. Industr. Math., 13:2 (2019), 340–349
\Bibitem{Sir19}
\by D.~T.~Siraeva
\paper The canonical form of the rank 2 invariant submodels of evolutionary type in ideal hydrodynamics
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 2
\pages 70--80
\mathnet{http://mi.mathnet.ru/sjim1044}
\crossref{https://doi.org/10.33048/sibjim.2019.22.207}
\elib{https://elibrary.ru/item.asp?id=41637774}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 2
\pages 340--349
\crossref{https://doi.org/10.1134/S1990478919020157}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067307784}
Linking options:
https://www.mathnet.ru/eng/sjim1044
https://www.mathnet.ru/eng/sjim/v22/i2/p70
This publication is cited in the following 5 articles:
Dilara Siraeva, “Partially invariant solution with an arbitrary surface of blow-up for the gas dynamics equations admitting pressure translation”, International Journal of Non-Linear Mechanics, 2024, 104904
Renata Nikonorova, Dilara Siraeva, Yulia Yulmukhametova, “New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations”, Mathematics, 10:1 (2022), 123
D. T. Siraeva, “Invariant Solutions of the Gas Dynamics Equations From 4-Parameter Three-Dimensional Subalgebras Containing All Translations in Space and Pressure Translation”, Sib. Electron. Math. Rep., 18:2 (2021), 1639–1650
D Siraeva, “Invariant submodel of rank 1 and two families of exact solutions of gas dynamics equations with an equation of state of the special form”, J. Phys.: Conf. Ser., 2099:1 (2021), 012017
D T Siraeva, “Two invariant submodels of rank 1 of the hydrodynamic type equations and exact solutions”, J. Phys.: Conf. Ser., 1666:1 (2020), 012049
Citation in format AMSBIB
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