2016/02/09 by Olivier Glass, Glass, O., Thierry Horsin +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Micro and Nano Robotics #Navier-Stokes equation solutions #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1602.03045
openalex publication_date 2016/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we establish a result of Lagrangian controllability for a fluid at low Reynolds number, driven by the stationary Stokes equation. This amounts to the possibility of displacing a part of a fluid from one zone to another by suitably using a boundary control. This relies on a weak variant of the Runge-Walsh's theorem (on approximation of harmonic functions) concerning the Stokes equation. We give two variants of this result, one of which we believe to be better adapted to numerical simulations.