TY - JOUR

T1 - Relativistic hydrodynamics of quark-gluon plasma and stability of scaling solutions

AU - Kouno, Hiroaki

AU - Maruyama, Masahiro

AU - Takagi, Fujio

AU - Saito, Koichi

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.41.2903

DO - 10.1103/PhysRevD.41.2903

M3 - Article

AN - SCOPUS:0008442316

VL - 41

SP - 2903

EP - 2911

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 9

ER -