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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)

Research Profile:

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.

Research Areas:

Fluid-structure interaction problems: This type of problems are usually modeled by the coupling of the Navier-Stokes equations (for the uid part) with the Navier equations of linearized elasticity (for an elastic solid) and/or with the balances of linear and angular momentum (in case of a rigid body). The coupling is given by the boundary conditions at the uid-solid interface. Questions that we investigate include: existence, uniqueness, stability and asymptotic behaviour of solutions of the governing equations in di erent physical situations.

Energy harvesting: An energy harvester is a device that converts mechanical energy (usually generated by ambient vibrations, which would be otherwise wasted) to electrical energy. Sources of this free mechanical energy could be the motion of vehicles on bridges, buildings vibrations, ocean waves, or human locomotion. Our objective here is the analysis and optimal design of underwater or wave energy harvesting devices.

Partially dissipative systems: From the point of view of the analysis of partial di erential equations, the above problems feature a dissipativeconservative interplay because some variables show some decay in time (like the kinetic energy of a viscous uid), whereas others have constant magnitude (like the angular momentum of a uid- lled undamped pendulum). This feature arises in many other problems characterized by the coupling of parabolic and hyperbolic partial di erential equations. For these equations many de nitions of solutions can be given ( strong , mild , weak , or very weak ). We would like to study properties of these solutions like regularity, stability, and asymptotic behaviour, by analyzing the governing equations in di erent functional settings.