Giusy Mazzone (Queen’s)

PDEs & Applications Seminar

Tuesday, November 7th, 2023

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Giusy Mazzone (Queen’s)

Title: On the motion of a fluid-filled elastic solid

Abstract: In this talk, I will introduce the equations governing the motion of an elastic solid with a cavity filled by a viscous incompressible fluid. Under the continuum hypothesis, conservation of mass and balances of linear and angular momentum lead to a system of partial differential equations (PDEs) governing the motion of the fluid-solid system. From the analytical point of view, these equations form a system of hyperbolic-parabolic PDEs, with the hyperbolic equations being the so-called Navier equations of linearized elasticity, whereas the parabolic equations are the Navier-Stokes equations for a viscous incompressible fluid. We will then discuss the existence and uniqueness of solutions of these equations.