Suppression of singularities of solutions of the Euler-Poisson system with density-dependent damping

TL;DR

This paper establishes a precise condition on density-dependent damping in a 1D Euler-Poisson system that prevents singularity formation, enabling control over plasma oscillations.

Contribution

It provides a sharp criterion for damping that suppresses singularities in solutions of the Euler-Poisson system with smooth initial data.

Findings

Identifies a critical damping condition for singularity suppression.

Demonstrates control over plasma oscillation breakdown.

Applicable to cold plasma in physics contexts.

Abstract

We find a sharp condition on the density-dependent coefficient of damping of a one-dimensional repulsive Euler-Poisson system, which makes it possible to suppress the formation of singularities in the solution of the Cauchy problem with arbitrary smooth data. In the context of plasma physics, this means the possibility of suppressing the breakdown of arbitrary oscillations of cold plasma.