Special Session 98: Control, Inverse problems and Long time dynamics of Evolutionary Systems

Implications of a Novel Pressure Elimination Method for a Certain Nonlinear Fluid-Structure PDE Interaction
George Avalos
University of Nebraska-Lincoln
USA
Co-Author(s):    Yuhao Mu
Abstract:
In this talk we present some implications of our new technique for eliminating and recovering the pressure for a particular fluid-structure interaction model, a technique which is valid for general bounded Lipschitz domains. The specific fluid-structure interaction (FSI) that we consider is a well-known model of coupled Navier-Stokes flow with linear elasticity. The coupling between these two distinct PDE dynamics occurs across a boundary interface, with each of the components evolving on its own distinct geometry, and with the boundary interface being Lipschitz. Among other consequences,the new pressure elimination technique leads to a proof of well-posedness of the PDE system, globally in time in 2D (and 3D with small data assumptions), with again, this wellposedness being valid for general Lipschitz geometries.