Relativistic hydrodynamics of quark-gluon plasma and stability of scaling solutions

Hiroaki Kouno, Masahiro Maruyama, Fujio Takagi, Koichi Saito

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41 Citations (Scopus)


The scaling solutions of the relativistic hydrodynamics are expected to play an important role in describing the expansion stage of a quark-gluon plasma which may be formed in nucleus-nucleus collisions at high energies. After summarizing some general properties of the scaling solutions, we study in detail their stability against small perturbations. In some typical cases of the two-dimensional scaling solution it is found that (i) the scaling solution is stable if the Reynolds number R defined in terms of the viscosity coefficients is larger than a critical value Rc (=1), (ii) it is also stable for a long-wavelength perturbation if R is small enough, and (iii) it becomes unstable when R approaches Rc from below. It is also shown that these results are related to the time dependence of the Reynolds number, the entropy density, and the temperature, and the point R=Rc corresponds to a critical instant when the heating due to the dissipative processes balances with the cooling due to the expansion of the fluid. The stability of the scaling solution of the quark-gluon plasma is examined for typical ranges of the relevant parameters.

Original languageEnglish
Pages (from-to)2903-2911
Number of pages9
JournalPhysical Review D
Issue number9
Publication statusPublished - 1990

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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