Regularizing factors for the Euler-Poisson equations

TL;DR

This paper reviews how adding specific regularizing factors to the Euler-Poisson equations without pressure can delay or prevent finite-time solution singularities, summarizing recent and existing results.

Contribution

It provides a comprehensive review of regularizing factors that influence the smoothness and longevity of solutions to the Euler-Poisson equations without pressure.

Findings

Certain regularizing terms can prevent finite-time blow-up

Review of recent advances in the field

Identification of conditions delaying singularity formation

Abstract

he Cauchy problem for the Euler-Poisson equations without pressure is considered and the question of what additional terms added to the system can delay or completely prevent the loss of smoothness of the solution in a finite time is studied. We review already published and recent results in this field.