Talks

Abstract. These lectures are devoted to some properties of periodic composites in electrophysics. On the one hand, the characterization of smooth periodic electric fields among the set of smooth periodic gradients fields is investigated. The laminate fields are also studied in this perspective. On the other hand, the study of the Hall effect in composites shows a gap between the dimension two preserving the bounds of the Hall coefficient, and the dimension three involving unexpected effective properties.
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Abstract. We study a fluid-structure system describing the motion of an elastic solid inside an incompressible viscous fluid in three dimensions. The motion of the solid is described by the Lamé system of linear elasticity and the fluid obeys the incompressible Navier-Stokes equations in a time-dependent domain. At the fluid-solid interface, natural conditions are imposed, continuity of the velocities and of the Cauchy stress forces. The fluid and the solid are coupled through these conditions. By this interaction, the fluid deforms the boundary of the solid which in turn influences the fluid motion. We prove the existence and uniqueness of local strong solutions by rewriting the coupled system in Lagrangian variables and by using the method of successive approximations. Our analysis relies on new regularity results for the linearized coupled system. This is a joint work with M. Vanninathan from TIFR CAM, Bangalore.