The Euler relativistic gasdynamic system. Chaplygin–Kármán–Tsien laws and substitution principle

  • Colin Rogers

    University of New South Wales, Sydney, Australia
  • Tommaso Ruggeri

    Università di Bologna, Bologna, Italy; Accademia Nazionale dei Lincei, Rome, Italy
The Euler relativistic gasdynamic system. Chaplygin–Kármán–Tsien laws and substitution principle cover
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Abstract

A seed class of exact solutions of the Euler system of two-dimensional relativistic gasdynamics is derived with an underlying Chaplygin–Kármán–Tsien type constitutive law. The invariance of the nonlinear relativistic system under multi-parameter reciprocal Bäcklund transformations is applied to generate a wide class of novel associated solutions with a barotropic relation. The latter reduces to the standard Chaplygin–Kármán–Tsien gas law in the non-relativistic limit. An additional invariance of the general relativistic gasdynamics system is established under a substitution principle. The latter represents an extension of a classical result in non-relativistic gasdynamics.

Cite this article

Colin Rogers, Tommaso Ruggeri, The Euler relativistic gasdynamic system. Chaplygin–Kármán–Tsien laws and substitution principle. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 35 (2024), no. 3, pp. 447–457

DOI 10.4171/RLM/1047