We investigate the existence of a drag-minimizing shape for two classes of optimal-design problem of fluid mechanics, namely the vector Burgers equations and the Navier-Stokes equations. It is known that the two-dimensional Navier-Stokes problem of shape optimization has a solution in any class of domains with at most l holes. We show, for the Burgers equation in three dimensions, that the existence of a minimizer still holds in the classes Ocr and W introduced by Bucur and Zolesio. These classes are defined by means of capacitary constraints at the boundary. For the 3D Navier-Stokes equations we prove some results of existence of drag-minimizing shape, under additional assumptions on the class of domains to be considered. We also discuss how these assumptions critically depend on the definition of weak solutions for Navier-Stokes equations and, more specifically, on the characterization of the spaces in which it is possible to prove the uniqueness for the linear Stokes problem.

Some problems of shape optimization arising in stationary fluid motion

BERSELLI, LUIGI CARLO;
2004-01-01

Abstract

We investigate the existence of a drag-minimizing shape for two classes of optimal-design problem of fluid mechanics, namely the vector Burgers equations and the Navier-Stokes equations. It is known that the two-dimensional Navier-Stokes problem of shape optimization has a solution in any class of domains with at most l holes. We show, for the Burgers equation in three dimensions, that the existence of a minimizer still holds in the classes Ocr and W introduced by Bucur and Zolesio. These classes are defined by means of capacitary constraints at the boundary. For the 3D Navier-Stokes equations we prove some results of existence of drag-minimizing shape, under additional assumptions on the class of domains to be considered. We also discuss how these assumptions critically depend on the definition of weak solutions for Navier-Stokes equations and, more specifically, on the characterization of the spaces in which it is possible to prove the uniqueness for the linear Stokes problem.
2004
Berselli, LUIGI CARLO; Guasoni, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/83627
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