Abstract
For the submodel of helical motions invariant with respect to the sum of rotation and translation, we consider solutions with pressure and density depending on time alone. Consistency of the system is studied by proceeding to Lagrangian variables. Equivalence of solutions is determined in terms of the five-dimensional admissible group. All solutions of the form described are calculated to within equivalence.
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References
L. V. Ovsyannikov, “Program ‘Submodels.’ Gas dynamics,”Prikl. Mat. Mekh. [Appl. Math. Mech.],58, No. 4, 30–55 (1994).
L. V. Ovsyannikov,Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).
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Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 133–141, January, 1996.
The work was financially supported by the Russian Foundation for Basic Research under grant No. 93-013-17326.
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Khabirov, S.V. Gas-dynamic helical motions with pressure and density depending on time alone. Math Notes 59, 97–103 (1996). https://doi.org/10.1007/BF02312470
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DOI: https://doi.org/10.1007/BF02312470