One-dimensional optimal system for 2D Rotating Ideal Gas

Abstract

We derive the one-dimensional optimal system for a system of three partial differential equations which describe the two-dimensional rotating ideal gas with polytropic parameter $\gamma >2.$ The Lie symmetries and the one-dimensional optimal system are determined for the nonrotating and rotating systems. We compare the results and we found that when there is no Coriolis force the system admits eight Lie point symmetries, while the rotating system admits seven Lie point symmetries. Consequently the two systems are not algebraic equivalent as in the case of $\gamma =2$ which was found by previous studies. For the one-dimensional optimal system we determine all the Lie invariants, while we demonstrate our results by reducing the system of partial differential equations into a system of first-order ordinary differential equations which can be solved by quadratures.

17 pages, to appear in Symmetry (MDPI) in the special issue: Symmetry in Applied Mathematics

References in corpus (2)

• A direct algorithm of one-dimensional optimal system for the group invariant solutions
• Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes

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