A class of global solutions to the Euler-Poisson system

Abstract

Using recent developments in the theory of globally defined expanding compressible gases, we construct a class of global-in-time solutions to the compressible 3-D Euler-Poisson system without any symmetry assumptions in both the gravitational and the plasma case. Our allowed range of adiabatic indices includes, but is not limited to all $\gamma$ of the form $\gamma =1+\frac{1}{n}$, $n\in \mathbb{N}\setminus \{1\}$. The constructed solutions have initially small densities and a compact support. As $t\to \infty$ the density scatters to zero and the support grows at a linear rate in $t$.

29 pages

References in corpus (3)

• Expansion of a compressible gas in vacuum
• Expanding large global solutions of the equations of compressible fluid mechanics
• Non-neutral global solutions for the electron Euler-Poisson system in 3D