Threshold phenomenon in n-dimensional repulsive restricted Euler–Poisson equations with time-dependent damping

Abstract

The damping term has an important effect on the existence of solution in fluid dynamics. In this paper, we will consider the threshold phenomenon of global existence and blow up of solution in multi-dimensional restricted Euler–Poisson equations with time-dependent damping. Using the method of functional construction, we will provide the upper threshold for blow up of solutions in finite time and subthresholds for the global existence of solutions of n-dimensional repulsive restricted Euler–Poisson equations with time-dependent damping under the appropriate assumptions on initial data.