# Giusy Mazzone

Assistant Professor (NTT) [AY '16-19]

#### Research Interests

Applied Mathematics, Mathematical Analysis, Partial Differential Equations, Dynamical Systems, Fluid Mechanics and Fluid Dynamics, Mathematical Physics, long-time behavior of solutions to fluid-solid interaction problems, attainability and stability of the equilibrium configurations. Approximation Theory, behavior of interpolating operators on discontinuous functions and approximation of cosine functions by iterates of bounded linear operators.

#### Publications

*On the motion of two rigid bodies with a fluid-filled gap*, in preparation.

- (with J. Prüss and G. Simonett)
*On the motion of a fluid-filled rigid body with Navier boundary conditions*, submitted (2018). https://arxiv.org/abs/1809.03852

- (with J. Prüss and G. Simonett)
*A maximal regularity approach to the study of motion of a rigid body with a fluid-filled cavity*, submitted (2018). https://arxiv.org/abs/1804.05403

- (with G. P. Galdi)
*Stability and long-time behavior of a pendulum with an interior cavity filled with a viscous liquid*. RIMS Kôkyûroku Proceedings No. 2058,*Mathematical Analysis of Viscous Incompressible Fluid*, 2018, 90--107.

- (with G.P. Galdi and M. Mohebbi)
*On the motion of a liquid-filled heavy body around a fixed point*. Quart. Appl. Math., 76 (1), (2018) pp. 113-145. Published electronically on October 4, 2017.

- (with K. Disser, G.P. Galdi, and P. Zunino)
*Inertial motions of a rigid body with a cavity filled with a viscous liquid*. Arch. Rational Mech. Anal., 221 (1), (2016) 487-526.

- (with G.P. Galdi)
*On the motion of a pendulum with a cavity entirely filled with a viscous liquid*. Recent progress in the theory of the Euler and Navier-Stokes Equations, London Mathematical Society Lecture Note Series: 430, Cambridge University Press, 2016, pp. 37-56.

- (with G.P. Galdi and M. Mohebbi)
*On the motion of a liquid-filled rigid body subject to a time-periodic torque*. Ch. in Recent Developments of Mathematical Fluid Mechanics, Springer Basel, Basel, 2016, pp. 233-255.

- (with G.P. Galdi and P. Zunino)
*Inertial Motions of a Rigid Body with a cavity filled with a viscous liquid*. https://arxiv.org/abs/1405.6596 (2014).

- (with G.P. Galdi and P. Zunino)
*Inertial motions of a rigid body with a cavity filled with a viscous liquid*. Comptes Rendus Mécanique 341, (2013) 760–765.

- (with M. Campiti and C. Tacelli)
*On the interpolation of discontinuous functions*. Journal of Approximation Theory 164, (2012) 731–753.

- (with M. Campiti and C. Tacelli)
*Approximation of cosine functions and Rogosinski type operators*. Studia Universitatis Babeş-Bolyai. Mathematica 56, (2011) 261–272.

- (with M. Campiti and C. Tacelli)
*Behavior of bivariate interpolation operators at points of discontinuity of the first kind*. Note di Matematica dell’Università del Salento 31, (2011) 43–66.

#### Conference Talks

*On the stability and long-time behavior of fluid-solid systems.*Applied Math Colloquium, Penn State University, November 26, 2018.*On the inertial motion of a fluid-filled rigid body with Navier boundary conditions*. Special Session: Recent Advances in Mathematical Fluid Mechanics, AMS Fall Southeastern Sectional Meeting, University of Arkansas, November 3-4, 2018.*On the inertial motion of a fluid-filled rigid body with partial-slip boundary conditions*. Special Session: Recent Developments in Mathematical Analysis of Some Nonlinear Partial Differential Equations, AMS Fall Central Sectional Meeting, University of Michigan, October 20-21, 2018.*On the motion of rigid bodies with a fluid-filled gap*. Special Session: Partial Differential Equations and New Perspective of Variational Methods, AMS Spring Southeastern Sectional Meeting, Vanderbilt University, April 14-15, 2018.*Long-time behavior and stability of rigid bodies with a fluid-filled gap*. MS14: Free Boundary Problems and Fluid Interfaces, SIAM Conference on Analysis of Partial Differential Equations 2017, The Baltimore Convention Center, Baltimore USA, December 9-12, 2017.*Stability and long-time behavior of a heavy rigid body with a cavity completely filled with a viscous liquid*. 2017 Midwestern Workshop on Asymptotic Analysis, IUPUI Indianapolis, USA, October 6-8, 2017.*Long-time behavior of rigid bodies with a fluid-filled gap*. Special Session: Free-boundary Fluid Models and Related Problems, AMS Spring Southeastern Sectional Meeting, College of Charleston, Charleston USA, March 10-12, 2017.*Asymptotic behavior of rigid bodies with a liquid-filled gap*.*On the motions of a liquid-filled rigid body around a fixed point.*International Conference on Evolution Equations, Vanderbilt University, Nashville USA, May 16-20, 2016.*On the motions of a liquid-filled pendulum.*Conference Numerical Analysis and Predictability of Fluid Motion, Department of Mathematics, University of Pittsburgh, USA, May 3-4, 2016.*On the inertial motions of liquid-filled rigid body with slip boundary conditions.*Particles in Flows, Summer School & Workshop, Institute of Mathematics of the Academy of Sciences of Czech Republic, Prague Czech Republic, August 25-31, 2014.*On the dynamics of a fluid-filled rigid body: inertial and periodic motions.*Seminar at the Department of Mathematics and Physics, Università del Salento, Lecce Italy, July 1, 2013.*Inertial motions of a rigid body with a liquid-filled cavity.*Workshop on Navier-Stokes Equations, Institute for Mathematics RWTH Aachen University, Aachen Germany, May 21-24, 2013.*On the inertial motions of fluid-filled rigid body with slip boundary conditions.*The 34th Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE 2014), The University of Memphis, Memphis USA, October 11-12, 2014.*On the inertial motions of liquid-filled rigid bodies.*66th Annual Meeting of the APS Division of Fluid Dynamics, Pittsburgh USA, November 24-26, 2013.*On the interpolation of discontinuous functions.*Second International Conference on Numerical Analysis and Approximation Theory (NAAT 2010), Babeș-Bolyai University, Department of Applied Mathematics of Faculty of Mathematics and Computer Science, Cluj-Napoca Romania, September 23-26, 2010.

#### Grants

#### Teaching

MATH 3100/5100 - Introduction to Analysis (Instructor)