Applied Mathematics Colloquium: Dr. Giusy Mazzone
Abstract: In this talk I will introduce a variety of fluid-solid interaction problems, and discuss stability and long-time behavior of the motions. We will focus on interactions between fluids and rigid bodies. The governing equations feature the coupling of the Navier-Stokes equations with the balance of momentums for the solids. Such equations have a "partially dissipative" nature due to the interplay between an energy functional that is non-increasing along the trajectories and certain quantities (depending on the solution) that are conserved at all times. We will investigate this dissipative-conservative interplay in the context of stabilization problems, i.e., convergence of motions to steady states. The method we employ is based on a spectral stability analysis of the equations in combination with a "generalized linearization principle" for evolution equations possessing a stable (���attracting") manifold.