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

2025/08/07 by Francfort, Gilles A., Giacomini, Alessandro, Weady, Scott
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.05481

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.

Citations

• The hydrodynamics of swimming microorganisms

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