DOI: https://doi.org/10.30970/jps.09.233
ULTRA-RELATIVISTIC EXPANSION OF IDEAL FLUID WITH LINEAR EQUATION OF STATE
V. I. Zhdanov, M. S. Borshch
Taras Shevchenko National University of Kyiv
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Journal of Physical Studies 9(3), 233–237 (2005)
DOI: https://doi.org/10.30970/jps.09.233 ULTRA-RELATIVISTIC EXPANSION OF IDEAL FLUID WITH LINEAR EQUATION OF STATEV. I. Zhdanov, M. S. Borshch Taras Shevchenko National University of Kyiv |
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We study solutions of the relativistic hydrodynamic equations, which describe spherical or cylindrical expansion of ideal fluid. We derived approximate solutions involving two arbitrary functions which describe the asymptotic behaviour of expanding fireballs in ultra-relativistic limit. In the case of a linear equation of state $p(ε )= κ ε - c_1 $, $ (0<κ<1)$ we show that the solution may be represented in form of an asymptotic series in negative powers of radial variable; recurrence relations for the coefficients are obtained. This representation is effective if $κ > 1/(2J+1)$ ($J=2$ for spherical expansion and $J=1$ for the cylindrical one); in this case the approximate solutions have a wave-like behaviour.
PACS number(s): 47.75.+f