Formation of singularities of solutions to the three-dimensional Euler-Boltzmann equations in radiation hydrodynamics

The Cauchy problem for the three-dimensional Euler-Boltzmann equations of a polytropic, ideal and isentropic fluid in radiation hydrodynamics is considered. The formation of singularities in smooth solutions is studied. It is proved that some C(1) solutions, regardless of the size of the initial disturbance, will develop singularities in a finite time provided that the initial disturbance satisfies certain conditions.