Formation of Singularities in Compressible Euler–Poisson Fluids with Heat Diffusion and Damping Relaxation

We are concerned with a coupling effect of heat diffusion, damping relaxation, and electric potential on the large-time behavior of solutions of the compressible Euler–Poisson fluids starting with smooth initial data. In this paper we prove that, for smooth initial data with large C1norm, the corresponding solution will develop singularities in finite time. This fact indicates that this coupling effect is not strong enough to prevent the formation of singularities and the development of shock waves in compressible Euler–Poisson fluids as time evolves.