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Self-Similar Solutions to the Spherically-Symmetric Euler Equations with a Two-Constant Equation of State

Author

Listed:
  • Qitao Zhang

    (Hangzhou Normal University)

  • Yanbo Hu

    (Hangzhou Normal University)

Abstract

This paper is concerned with self-similar flows of the multidimensional isentropic compressible Euler equations caused by the uniform expansion of a spherically-symmetric piston into the undisturbed fluid. Under the spherically-symmetric and self-similar assumptions, the problem can be reduced to a boundary value problem for a system of nonlinear ordinary differential equations. We consider the two-constant equation of state $$p = {A_1}{\rho ^{\gamma 1}} + {A_2}{\rho ^{\gamma 2}}$$ p = A 1 ρ γ 1 + A 2 ρ γ 2 which arises in a number of various physical contexts and results the problem becomes more complicated than the case of polytropic gas equation of state. To deal with the difficulty, we first establish the global existence of smooth solutions to the boundary value problem for a new ODE system.

Suggested Citation

  • Qitao Zhang & Yanbo Hu, 2019. "Self-Similar Solutions to the Spherically-Symmetric Euler Equations with a Two-Constant Equation of State," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(1), pages 35-49, March.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:1:d:10.1007_s13226-019-0305-z
    DOI: 10.1007/s13226-019-0305-z
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