Dissipative hydrodynamics for viscous relativistic fluids

Abstract

Explicit equations are given for describing the space-time evolution of non-ideal (viscous) relativistic fluids undergoing boost-invariant longitudinal and arbitrary transverse expansion. The equations are derived from the second-order Israel-Stewart approach which ensures causal evolution. Both azimuthally symmetric (1+1)-dimensional and non-symmetric (2+1)-dimensional transverse expansion are discussed. The latter provides the formal basis for the hydrodynamic computation of elliptic flow in relativistic heavy-ion collisions including dissipative effects.

12 pages, no figures. Submitted to Physical Review C

References in corpus (4)

• Apparent Thermalization due to Plasma Instabilities in Quark-Gluon Plasma
• Hard-Loop Dynamics of Non-Abelian Plasma Instabilities
• Dynamics of Quark-Gluon-Plasma Instabilities in Discretized Hard-Loop Approximation
• Hydrodynamics at RHIC -- how well does it work, where and how does it break down?

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