Communications in Mathematical Sciences
Volume 20 (2022)
Necessary conditions for blow-up solutions to the restricted Euler–Poisson equations
Pages: 327 – 357
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.
restricted Euler–Poisson dynamics, blow-up solutions, asymptotic behaviors
2010 Mathematics Subject Classification
Liu was partially supported by the National Science Foundation under Grant DMS1812666.
Shin was supported by newly appointed professor research fund of Hanbat National University and the National Research Foundation under Grant NRF-2017R1E1A1A03070498.
Received 29 October 2019
Accepted 30 June 2021
Published 28 January 2022