Niveau: Supérieur, Doctorat, Bac+8
Titles and abstracts Mini-course Control of some fluid-structure interactions by Marius Tucsnak – Universite Henri Poincare, Nancy, France Abstract: In many practical problems a fluid interacts with a solid structure, exerting stresses that may cause deformation in the structure and, thus, alter the flow of the fluid itself. These phenomena are usually called fluid-structure interactions and they occur, for instance, in aerodynamics (flow around an aircraft), medicine (blood flow in vessels), zoology (swimming of aquatic animals). The mathematical study of these problems rises several challenges, the main one being due to the fact that the domain filled by the fluid is one of the unknowns of the problem. Another difficulty which has to be tackled is that the dynamics of the system couples the ordinary or partial differential equations modeling the solid with the partial differential equations modeling the fluid. Within this work we focus on the coupled motion of a collection of solids and of a fluid surround- ing them. The solids are either rigid or they have a prescribed deformation law. According to the fact that the fluid ideal, viscous (compressible or incompressible) or non-Newtonian, the corresponding mathematical models are given by systems of partial and ordinary differential equations of increasing complexity. The common features of these models are the facts that the equations for the fluid and for the solids are coupled via the boundary conditions and that the equations for the fluid hold in a spatial domain which is variable with respect to time.
- relative velocity
- fluid-structure system
- equation governed
- navier-stokes fluid
- system unboundedness
- when both
- approximate controllability
- numerical results
- equation