Velocity optimization of self-equilibrated obstacles in a two-dimensional viscous flow

Gilles A. Francfort; Alessandro Giacomini; Scott Weady

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arXiv · 2508.05481

Velocity optimization of self-equilibrated obstacles in a two-dimensional viscous flow

Gilles A. Francfort·Alessandro Giacomini·Scott Weady

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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.

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Gilles A. Francfort, Alessandro Giacomini, Scott Weady. 2025-08-07. Velocity optimization of self-equilibrated obstacles in a two-dimensional viscous flow. https://arxiv.org/abs/2508.05481

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