chapter
20 Pages

## An Energy Principle for a Free Boundary Problem for Navier-Stokes Equations

WithRaja Dziri, Jean-Paul Zolésio

Abstract We study the existence of an optimal domain for an energy shape minimization problem.

By showing that the problem considered can be relaxed to measurable sets we avoid regularity hypotheses. The study leads, in the nonsmooth case, to a distributed optimality condition, which can be expressed, in the smooth case, by an extra-equation satisfied on the boundary of the optimal domain.