  A simple multi-physical system for the potential flow of a fluid through a
shroud in which a mechanical component, like a turbine vane, is placed, is
modeled mathematically. We then consider a multi criteria shape optimization
problem, when the shape of the component is allowed to vary under a certain set
of 2nd order H\"older continuous differentiable transformations of a baseline
shape with boundary of the same continuity class. As objective functions, we
consider a simple loss model for the fluid dynamical efficiency and the
probability of failure of the component due to repeated application of loads
that stem from the fluid's static pressure. For this multi-physical system, it
is shown that under certain conditions the Pareto front is maximal in the sense
that the Pareto front of the feasible set coincides with Pareto front of its
closure. We also show that the set of all optimal forms with respect to
scalarization techniques deforms continuously (in the Hausdorff metric) with
respect to preference parameters.
