The conservation laws and group properties of the equations of gas dynamics with zero velocity of sound |
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| Authors: | Yu A Chirkunov |
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| Institution: | 1. Department of Physics and Mathematics, Chelyabinsk State Pedagogical University, Chelyabinsk 454080, Russia;2. Department of Computational Mathematics and Informatics, South Ural State University, Chelyabinsk 454080, Russia;3. Department of Physics, South Ural State University, Chelyabinsk 454080, Russia;1. Center for Operations Research and Econometrics (CORE), Université Catholique de Louvain, Voie du Roman Pays 34, Louvain-la-Neuve B-1348, Belgium;2. Luxembourg Institute of Socio-Economic Research (LISER), 11 Porte des Sciences, Esch-sur-Alzette L-4366, Luxembourg;3. Department of Management, Università Ca’ Foscari, San Giobbe, Cannaregio 837, Venezia I-30121, Italy |
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| Abstract: | All the conservation laws of zero order are obtained by the method of A-operators for a system of n-dimensional (n ≥ 1) equations of gas dynamics with zero velocity of sound. A group subdivision is carried out of this system with respect to an infinite subgroup, which is a normal divider of its main Lie group of transformations; the main group of the resolving system is obtained. First-order non-local symmetries are obtained for the initial system. A special choice of the mass Lagrange variables enables this system to be converted to a reduced system equivalent to it, containing n - 1 spatial variables, which, for n = 2, is written in the form of a one-dimensional complex heat-conduction equation using complex dependent and independent variables. |
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