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On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior

Carrillo, JA; Choi, YP; Zatorska, E; (2016) On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior. Mathematical Models and Methods in Applied Sciences , 26 (12) pp. 2311-2340. 10.1142/S0218202516500548. Green open access

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Abstract

We analyze the one-dimensional pressureless Euler-Poisson equations with linear damping and nonlocal interaction forces. These equations are relevant for modeling 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.

Type: Article
Title: On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior
Open access status: An open access version is available from UCL Discovery
DOI: 10.1142/S0218202516500548
Publisher version: https://doi.org/10.1142/S0218202516500548
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Flocking; alignment; hydrodynamics; regularity; critical thresholds
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/10035987
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