Pressureless Euler alignment system with control
Analysis of PDEs
2018-02-01 v1 Mathematical Physics
math.MP
Numerical Analysis
Optimization and Control
Abstract
We study a non-local hydrodynamic system with control. First we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then discuss the critical thresholds that leading to global regularity or finite-time blow-up of strong solutions in one and two dimensions. Finally we propose a finite volume scheme for numerical solutions of the controlled system. Several numerical simulations are shown to validate the theoretical and computational results of the paper.
Cite
@article{arxiv.1801.10587,
title = {Pressureless Euler alignment system with control},
author = {Giacomo Albi and Young-Pil Choi and Axel-Stefan Haeck},
journal= {arXiv preprint arXiv:1801.10587},
year = {2018}
}