Formation of singularities in relativistic fluid dynamics and in   spherically symmetric plasma dynamics
  We prove that for large enough data, the life span of smooth solutions to the Cauchy problem for the following two quasilinear hyperbolic systems is finite: (1) equations of relativistic compressible fluid dynamics, (2) equations of plasma dynamics (Euler-Maxwell equations with background charge) in the spherically symmetric case. 
Yan Guo and A. Shadi Tahvildar-Zadeh