On the dynamical evolution of hot spots in powerful radio loud AGNs
  We describe the dynamical evolution of hot spots velocity, pressure and mass density in radio loud active galactic nuclei (AGNs), taking proper account of (1) the conservations of the mass, momentum, and kinetic energy flux of the unshocked jet, (2) the deceleration process of the jet by shocks, and (3) the cocoon expansion without assuming the constant aspect ratio of the cocoon. By the detailed comparison with two dimensional relativistic hydrodynamic simulations, we show that our model well reproduces the whole evolution of relativistic jets. Our model can explain also the observational trends of the velocity, the pressure, the size, and mass density of hot spots in compact symmetric objects (CSOs) and FR II radio galaxies. 
N. Kawakatu and M. Kino