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

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 m...

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Bibliographic Details
Published in:Physica. D 2022-01, Vol.429, p.133077, Article 133077
Main Author: Rozanova, Olga S.
Format: Article
Language:English
Subjects:
Density dependent damping
Equations of cold plasma
Euler–Poisson system
Singularity formation
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Summary: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. •Density-dependent damping can suppress singularities in the Euler–Poisson system.•A sharp characterization of the damping factor suppressing blowup is found.•Electron–ion collisions can completely eliminate the breakdown of oscillations in the cold plasma.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2021.133077