Existence of optimal boundary control for the Navier–Stokes equations with mixed boundary conditions

  • Telma Guerra

    Escola Superior de Tecnologia do Barreiro, Lavradio, Portugal
  • Adélia Sequeira

    Instituto Superior Técnico, Lisboa, Portugal
  • Jorge Tiago

    Instituto Superior Técnico, Lisboa, Portugal

Abstract

Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach allows to increase the accuracy of numerical simulations. In the particular case of fluid dynamics, it leads to optimal control problems with non-standard cost functionals which, when subject to the Navier-Stokes equations, require a non-standard theoretical frame to ensure the existence of solution. In this work, we prove the existence of solution for a class of such type of optimal control problems. Before doing that, we ensure the existence and uniqueness of solution for the 3D stationary Navier-Stokes equations, with mixed-boundary conditions, a particular type of boundary conditions very common in applications to biomedical problems.

Cite this article

Telma Guerra, Adélia Sequeira, Jorge Tiago, Existence of optimal boundary control for the Navier–Stokes equations with mixed boundary conditions. Port. Math. 72 (2015), no. 2/3, pp. 267–283

DOI 10.4171/PM/1968