Critical thresholds in Euler-Poisson equations

Critical Thresholds in Euler-Poisson Equations

We present a preliminary study of a new phenomena associated with the Euler-Poisson equations — the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the initial configuration crosses an intrinsic, O(1) critical threshold. We investigate a class of Euler-Poisson equations, ranging from one-dimensional problems...

Critical Thresholds in Euler-Poisson Equations

Critical Thresholds in 2D Restricted Euler-Poisson Equations

We provide a complete description of the critical threshold phenomena for the two-dimensional localized Euler-Poisson equations, introduced by the authors in [17]. Here, the questions of global regularity vs. finite-time breakdown for the 2D Restricted Euler-Poisson solutions are classified in terms of precise explicit formulae, describing a remarkable variety of critical threshold surfaces of ...

Thresholds in three-dimensional restricted Euler–Poisson equations

This work provides a description of the critical threshold phenomenon in multi-dimensional restricted Euler–Poisson (REP) equations, introduced in [H. Liu, E. Tadmor. Spectral dynamics of the velocity gradient field in restricted fluid flows, Comm. Math. Phys. 228 (2002) 435–466]. For three-dimensional REP equations, we identified both upper thresholds for the finite-time blow up of solutions a...

On the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behavior

We analyse the one-dimensional pressureless Euler-Poisson equations with a linear damping and non-local interaction forces. These equations are relevant for modelling collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and the subcritical region with global-in-time existence of the classical solution. We derive an...