Blow-up conditions for two dimensional modified Euler–Poisson equations

The multi-dimensional Euler–Poisson system describes the dynamic behavior of many important physical flows, yet as a hyperbolic system its solution can blow-up for some initial configurations. This article strives to advance our understanding on the critical threshold phenomena through the study of a two-dimensional modified Euler–Poisson system with a modified Riesz transform where the singularity at the origin is removed. We identify upper-thresholds for finite time blow-up of solutions for the modified Euler–Poisson equations with attractive/repulsive forcing.