On blowup phenomenon of solutions to the Euler equations for generalized chaplygin gas

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Abstract

We obtain some blowup results of the Euler equations for Generalized Chaplygin Gas (GCG). In particular, we show that the solutions with velocity of the form u(t, x) = a(t) ˙/ a(t) x blow up on finite time if the parameter of the ordinary differential equation related to a(t) is negative. Moreover, by the substitution and perturbation methods, we construct a family of non-spherical symmetric blowup solutions for the one dimensional GCG system. Copyright © 2016 Research India Publications.
Original languageEnglish
Pages (from-to)1-16
JournalAdvances in Theoretical and Applied Mathematics
Volume11
Issue number1
Publication statusPublished - 2016

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Chaplygin Gas
Euler Equations
Blow-up
Blow-up Solution
Perturbation Method
Substitution
Ordinary differential equation
Form
Family

Citation

Cheung, K. L. (2016). On blowup phenomenon of solutions to the Euler equations for generalized chaplygin gas. Advances in Theoretical and Applied Mathematics, 11(1), 1-16.

Keywords

  • Blowup
  • Spherical Symmetry
  • Euler equations
  • Trivial Solutions
  • Generalized
  • Chaplygin Gas