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<p>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.</p>

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Velocity Optimization of Self-Equilibrated Obstacles in A Two-Dimensional Viscous Flow

  • 期刊论文

  • 发表日期：

    2026年4月18日

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  • Gilles A Francfort,
  • Alessandro Giacomini,
  • Scott Weady

摘要

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.