|Jeffery Hall, Rm. 411
|Applied mathematics, partial differential equations, fluid dynamics, fluid-solid interactions, mathematical physics
Degrees & Accolades:
Ph.D. Mechanical Engineering (University of Pittsburgh, 2016)
Ph.D. Mathematics (Università del Salento, 2012)
M.Sc. (Università degli Studi di Bari, 2008)
B.Sc. (Università degli Studi di Bari, 2006)
My research focusses on the analysis of partial differential equations (PDEs) arising in fluid mechanics and mathematical physics. I am particularly interested in fluid-solid interaction problems and their applications in geophysics and engineering. From a mathematical point of view, the equations governing fluid-solid interactions possess all the mathematical features of the nonlinear PDEs describing the motion of viscous fluids (the Navier-Stokes equations). The lack of a proof for the uniqueness of solutions satisfying the energy balance together with a "chaotic'' behavior of weak solutions for finite time intervals play a fundamental role in our problems. In addition, the coupling of the Navier-Stokes equations with the equations describing the motion of solids features a combination of a dissipative component originating from the fluid, and a conservative or even excited component due the solid counterpart. This dissipative-conservative interplay arises in many other problems characterized by the coupling of parabolic and hyperbolic PDEs. Our investigations aim to answer fundamental questions concerning the existence and regularity properties of solutions to the equations governing the motion of fluid-solid systems, and to provide a detailed description of the stability properties and long-time behaviour of the motions.