Section: New Results
Participants : Julien Lequeurre, Jean-François Scheid.
In , we deal with shape optimization problem for a Stokes/elasticity system. The aim is to find the optimal shape of an elastic structure which minimizes an energy type functional. Results are obtained for a simplified free-boundary one-dimensional problem.
In , we design a hilbertian framework for the analysis of the planar Navier-Stokes (NS) equations either in vorticity or in stream function formulation. The fluid is assumed to occupy a bounded possibly multiply connected domain. The velocity field satisfies either homogeneous (no-slip boundary conditions) or prescribed Dirichlet boundary conditions. We prove that the proposed approach is equivalent to the classical one (stated in primitive variables, i.e. velocity and pressure fields) for strong and weak solutions. In particular . In particular, in both cases, we retrieve the pressure from the vorticity or the current function.