Critical thresholds in pressureless Euler--Poisson equations with
background states
Critical thresholds in pressureless Euler--Poisson equations with
background states
We investigate the critical threshold phenomena in a large class of one dimensional pressureless Euler--Poisson (EP) equations, with non-vanishing background states. First, we establish local-in-time well-posedness in proper regularity spaces, which are adapted for a certain \textit{neutrality condition} to hold. The neutrality condition is shown to be necessary: we construct …