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arXiv · 1604.05229

On the pressureless damped Euler-Poisson equations with non-local forces: Critical thresholds and large-time behavior

José A. Carrillo·Young-Pil Choi·Ewelina Zatorska
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Abstract

We analyse the one-dimensional pressureless Euler-Poisson equations with a linear damping and non-local interaction forces. These equations are relevant for modelling collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and the subcritical region with global-in-time existence of the classical solution. We derive an explicit form of solution in Lagrangian coordinates which enables us to study the time-asymptotic behavior of classical solutions with the initial data in the subcritical region.

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José A. Carrillo, Young-Pil Choi, Ewelina Zatorska. 2016-04-18. On the pressureless damped Euler-Poisson equations with non-local forces: Critical thresholds and large-time behavior. https://arxiv.org/abs/1604.05229

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