Pressureless Euler alignment system with control

Giacomo Albi, Young Pil Choi, Axel Stefan Häck

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 lead to global regularity or finite-time blow-up of strong solutions in one and two dimensions. Finally, we use a finite volume scheme, coupled with an implicit-explicit time integrator to solve numerically the stiff scale of the controlled system. Several numerical simulations are shown to validate the theoretical and computational results of the paper.

Original languageEnglish
Pages (from-to)1635-1664
Number of pages30
JournalMathematical Models and Methods in Applied Sciences
Volume28
Issue number9
DOIs
Publication statusPublished - 2018 Aug 1

Fingerprint

Euler
Alignment
Critical Threshold
Global Regularity
Finite Time Blow-up
Optimal Approximation
Finite Volume Scheme
Dynamic Control
Strong Solution
One Dimension
Optimal Control Problem
Computational Results
Hydrodynamics
Two Dimensions
Numerical Simulation
Computer simulation

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

Albi, Giacomo ; Choi, Young Pil ; Häck, Axel Stefan. / Pressureless Euler alignment system with control. In: Mathematical Models and Methods in Applied Sciences. 2018 ; Vol. 28, No. 9. pp. 1635-1664.
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Pressureless Euler alignment system with control. / Albi, Giacomo; Choi, Young Pil; Häck, Axel Stefan.

In: Mathematical Models and Methods in Applied Sciences, Vol. 28, No. 9, 01.08.2018, p. 1635-1664.

Research output: Contribution to journalArticle

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