Finite propagation speed and finite time blowup of the Euler equations for generalized chaplygin gas

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Abstract

The blowup phenomenon for the N-dimensional isentropic compressible Euler equations for generalized chaplygin gas (GCG), which arises in a cosmology model related to dark matter and dark energy, is investigated. First, we establish the finite propagation speed property for the system. This allows one to apply the integration method to study the blowup problem. More precisely, by deriving a differential inequality, we show the any C¹ solution in a designed non-empty space blows up on finite time provided that the initial functional is sufficiently large. Copyright © 2017 Research India Publications.
Original languageEnglish
Pages (from-to)51-63
JournalAdvances in Theoretical and Applied Mathematics (ATAM)
Volume12
Issue number1
Publication statusPublished - 2017

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Chaplygin Gas
Finite Time Blow-up
Propagation Speed
Euler Equations
Blow-up
Compressible Euler Equations
Differential Inequalities
Dark Energy
Dark Matter
Cosmology
Model

Citation

Cheung, K. L. (2017). Finite propagation speed and finite time blowup of the Euler equations for generalized chaplygin gas. Advances in Theoretical and Applied Mathematics, 12(1), 51-63.

Keywords

  • Blowup
  • Euler equations
  • Chaplygin
  • Finite propagation speed