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arXiv · 2107.04155

Necessary conditions for blow-up solutions to the restricted Euler--Poisson equations

Hailiang Liu·Jaemin Shin
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Abstract

In this work, we study the behavior of blow-up solutions to the multidimensional restricted Euler--Poisson equations which are the localized version of the full Euler--Poisson system. We provide necessary conditions for the existence of finite-time blow-up solutions in terms of the initial data, and describe the asymptotic behavior of the solutions near blow up times. We also identify a rich set of the initial data which yields global bounded solutions.

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Hailiang Liu, Jaemin Shin. 2021-07-09. Necessary conditions for blow-up solutions to the restricted Euler--Poisson equations. https://doi.org/10.4310/cms.2022.v20.n2.a2

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