We discuss the nonlinear evolution of the Weibel instability of
electron beams in the relativistic and non-relativistic regimes in the
of a two-fluid description. We show the presence of two singularities per
responsible for the formation of very large density spikes. In the case
non-symmetric beams, we observe the compressive wave-break of the fast
population, and the generation of a dipolar magnetic field associated with
fast thin current and two larger slow return currents. This structure is
to those observed in PIC simulations of laser-plasma interactions.