Formation of singularities of solutions to the IBVP of the Euler–Boltzmann equations

The initial-boundary value problem for the three-dimensional Euler–Boltzmann equations of a polytropic, ideal and isentropic fluid in radiation hydrodynamics is considered outside a unit ball. It is proved that some $$C^{1}$$ solution will develop singularities in a finite time provided that a weighed functional associated with the initial momentum and the initial intensity of radiation is large.