  A formalism for anisotropic fluid dynamics is proposed. It is designed to
describe boost-invariant systems with anisotropic pressure. Such systems are
expected to be produced at the early stages of relativistic heavy-ion
collisions, when the timescales are too short to achieve equal thermalization
of transverse and longitudinal degrees of freedom. The approach is based on the
energy-momentum and entropy conservation laws, and may be regarded as a minimal
extension of the boost-invariant standard relativistic hydrodynamics of the
perfect fluid. We show how the formalism may be used to describe the
isotropization of the system (the transition from the initial state with no
longitudinal pressure to the final state with equal longitudinal and transverse
pressure).
