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.
|Number of pages||30|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 2018 Aug 1|
Bibliographical noteFunding Information:
G. A. is supported by GNCS–INDAM fundings, and by the project “MIUR Departments of Excellence 2018-2022”. Y.-P. C. is supported by National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (Nos. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. A.-S. H. acknowledges the support by DAAD–MIUR fundings.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics