Pressureless Euler alignment system with 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 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.