J4 ›› 2011, Vol. 46 ›› Issue (12): 104-107.

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Analytical blow-up solutions to the Euler equations

YAN Xiao-li, YUAN Bao-quan*   

  1. School of Mathematics and Information, Henan Polytechnic University, Jiaozuo 454000, Henan, China
  • Received:2010-09-30 Online:2011-12-20 Published:2011-12-24

Abstract:

A family of analytical solutions to the N dimensional isothermal Euler equations and the pressureless Euler equations with frictional damping are constructed by solving a second order ordinary differential equation. Especially, the solutions may blow up at a finite time T.

Key words:  blow-up solutions; isothermal Euler equations; frictional damping

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