#### Shape optimization for some wave resistance problems

We consider an immersed object moving at constant speed in calm water.

The water is seen as an incompressible inviscid fluid and the flow is

irrotationnal. The wave resistance is the drag force exerted by the

fluid on the object. This force is due to the presence of the

water/air interface (indeed, if there were only water, then

d’Alembert’s paradox would imply that this drag force is zero).

In this talk, we will consider two shape optimization problems related

to the wave resistance, from a theoretical and numerical point of

view. The first problem is the optimization of ship hulls in the

context of thin ships. In this case, Michell’s wave resistance formula

avoids to use the state equation. The second problem is a fully

immerged infinite cylinder. In this case, the state equation is the

Neumann-Kelvin problem