Chromohydrodynamic approach to the unstable quark-gluon plasma

We derive hydrodynamic-like equations that are applicable to short-time-scale color phenomena in the quark-gluon plasma. The equations are solved in the linear response approximation, and the gluon polarization tensor is derived. As an application, we study the collective modes in a two-stream system and find plasma instabilities when the fluid velocity is larger than the speed of sound in the plasma. The chromohydrodynamic approach, discussed here in detail, should be considered as simpler over other approaches and well-designed for numerical studies of the dynamics of an unstable quark-gluon plasma.