Velocity optimization of self-equilibrated obstacles in a two-dimensional viscous flow
Analysis of PDEs
2025-08-08 v1
Abstract
An obstacle is immersed in an externally driven 2D Stokes or Navier-Stokes fluid. We study the self-equilibration conditions for that obstacle under steady state assumptions on the flow. We then seek to optimize the translational and/or angular velocity of the obstacle by varying its shape. To allow general variations, we must consider a very large class of obstacles for which the notion of trace is meaningless. This forces us to revisit the notion of self-equilibration for both Stokes and Navier-Stokes in a measure theoretic environment.
Cite
@article{arxiv.2508.05481,
title = {Velocity optimization of self-equilibrated obstacles in a two-dimensional viscous flow},
author = {Gilles A. Francfort and Alessandro Giacomini and Scott Weady},
journal= {arXiv preprint arXiv:2508.05481},
year = {2025}
}