The Cauchy problem for a modified Euler-Poisson system in one dimension

Wei, Long

doi:10.1090/qam/1597

Author: Long Wei
Journal: Quart. Appl. Math. 79 (2021), 667-693
MSC (2020): Primary 35Q35, 35B44
DOI: https://doi.org/10.1090/qam/1597
Published electronically: June 1, 2021
MathSciNet review: 4328143
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Abstract: The aim of this paper is to investigate the Cauchy problem for a modified Euler-Poisson system (mEP) in one dimension. We first establish the local well-posedness of this system, and then show that a finite maximal life span for a solution necessarily implies wave breaking. Some sufficient conditions on the initial data that lead to finite time wave-breaking of solutions are given. In addition, we provide a persistence result for solutions of the mEP system in weighted $L^p$-spaces.

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