Euler-Poisson equations with velocity-dependent damping

We consider repulsive Euler-Poisson equations in both one-dimensional space and in the multidimensional case with radial symmetry, assuming a power-law velocity-dependent damping coefficient.

We show that under this assumption, in the one-dimensional case the set of initial data corresponding to a globally time-smooth solution expands, whereas in other dimensions (except for dimension 4) the damping does not influence on improving of smooth properties of the solution.

Namely, any arbitrary small perturbation of the steady state blow up, despite of its amplitude of oscillations decays.