Abstract :
The Cauchy problem is studied for a system of nonlinear partial differential
equations for some dissipative flows in Lagrangian formulation including heat
conduction, damping relaxation, and coupling to electric field. The well-posedness
of smooth solutions is investigated. It is proved that, for certain large initial data,
the solution will develop singularities and shock waves in finite time, which
indicates that the Cauchy problem does not have global smooth solutions even if
the initial data are smooth, and one has to seek weak solutions
