Section: New Results

Analysis and control of fluids and of fluid-structure interactions

In [38] , a new characteristics method for the discretization of the two dimensional fluid-rigid body problem is proposed in the case of different densities for the fluid and the solid. Convergence results are obtained for a fully-discrete finite element scheme.

In [35] , controllability results are obtained for a low Reynolds number swimmer. The swimmer is undergoing radial and axi-symmetric deformations in order to propel itself in a viscous fluid.

The aim of the paper [51] is to tackle the time optimal controllability of an (n+1)-dimensional nonholonomic integrator. A full description of the optimal control and optimal trajectories are explicitly obtained.

In [25] , we the interaction between a viscous incompressible fluid and an elastic structure immersed in the fluid.

In [30] , weconsider the model composed by a rigid body immersed into a n incompressible perfect fluid and analyze the regularity of the trajectory of the rigid body and of the fluid particles.

In [39] , we study the motion of a rigid body with a cavity filled with a viscous liquid.

In [34] , we analyze a model of vesicle moving into a viscous incompressible fluid.

In [27] , we obtain the identifiability of a rigid body moving in a stationary viscous fluid.

In [40] we study a mathematical model for the dynamics of vesicle membranes in a 3D incompressible viscous fluid. we show that, given $T>0$, for initial data which are small (in terms of $T$), these solutions are defined on $[0,T]$ (almost global existence).