English

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.

Keywords

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}
}
R2 v1 2026-07-01T04:39:17.070Z