
Andrea Giorgini Zorn Postdoctoral Fellow Department of Mathematics Indiana University
agiorgin(at)iu(dot)edu






Research Interests 

My research activity is focused on the study of nonlinear Partial Differential Equations arising from Fluid Mechanics, Biology and Materials Science.
I am currently interested in modeling and theoretical analysis of Diffuse Interface (Phase Field) problems describing the evolution of twophase fluid mixtures with complicated internal microstructures and driven by the surface tension.
My main research directions are:
NavierStokesCahnHilliard systems
HeleShaw and porous media flows with applications to tumor growth dynamics
Nonlocal models for longrange particle interactions
Multiphysics of complex fluids



Preprints 
 Continuous Data Assimilation for the 3D Ladyzhenskaya Model: Analysis and Computations
Y. Cao, A. Giorgini, M. Jolly & A. Pakzad
arXiv:2108.03513, 2021
 On the existence of strong solutions to the CahnHilliardDarcy system with mass source
A. Giorgini, K.F. Lam, E. Rocca & G. Schimperna
arXiv:2009.13344, 2020
 Diffuse interface models for incompressible binary fluids and the massconserving AllenCahn approximation
A. Giorgini, M. Grasselli & H. Wu
arXiv:2005.07236, 2020


Publications 
 Wellposedness of the twodimensional AbelsGarckeGrün model for twophase flows with unmatched densities
A. Giorgini
Calculus of Variations and Partial Differential Equations 60, 100 (2021)
 The NavierStokesCahnHilliard equations for mildly compressible binary fluid mixtures
A. Giorgini, R. Temam & X.T. Vu
Discrete & Continuous Dynamical Systems  B 26 (2021), 337366.
Special issue for the 20 years anniversary.
 Weak and strong solutions to the nonhomogeneous incompressible NavierStokesCahnHilliard system
A. Giorgini & R. Temam
Journal de Mathématiques Pure et Appliquées 144 (2020), 194249
 Wellposedness of a diffuse interface model for HeleShaw flows
A. Giorgini
Journal of Mathematical Fluid Mechanics 22, 5 (2020)
 Wellposedness for the BrinkmanCahnHilliard system with unmatched viscosities
M. Conti & A. Giorgini
Journal of Differential Equations 268 (2020), 63506384
 Uniqueness and regularity for the NavierStokesCahnHilliard system
A. Giorgini, A. Miranville & R. Temam
SIAM Journal on Mathematical Analysis 51 (2019), 25352574
 The nonlocal CahnHilliardHeleShaw system with logarithmic potential
F. Della Porta, A. Giorgini & M. Grasselli
Nonlinearity 31 (2018), 48514881
 The CahnHilliardHeleShaw system with singular potential
A. Giorgini, M. Grasselli & H. Wu
Annales de l'Institut Henry Poincaré C, Analyse Non Linéaire 35 (2018), 10791118
 NavierStokesVoigt equations with memory in 3D lacking instantaneous kinematic viscosity
F. Di Plinio, A. Giorgini, V. Pata & R. Temam
Journal of Nonlinear Science 28 (2018), 653686
 The nonlocal CahnHilliard equation with singular potential: wellposedness, regularity and strict separation property
C.G. Gal, A. Giorgini & M. Grasselli
Journal of Differential Equations 263 (2017), 52535297
 The CahnHilliardOono equation with singular potential
A. Giorgini, M. Grasselli & A. Miranville
Mathematical Models and Methods in Applied Sciences 27 (2017), 24852510
 Phasefield crystal equation with memory
M. Conti, A. Giorgini & M. Grasselli
Journal of Mathematical Analysis and Applications 436 (2016), 12971331
 On the SwiftHohenberg equation with slow and fast dynamics: wellposedness and longtime behavior
A. Giorgini
Communications on Pure and Applied Analysis 15 (2016), 219241


Teaching 
Spring 2021: Indiana University, M301  Linear Algebra and Applications
Spring 2021: Indiana University, M119  Brief Survey of Calculus 1
Fall 2020: Indiana University, M441  Introduction to Partial Differential Equations with Applications 1
Spring 2020: Indiana University, M343  Introduction to Differential Equations with Applications 1 (two sections)
Fall 2019: Indiana University, M441  Introduction to Partial Differential Equations with Applications 1
Spring 2019: Indiana University, M365  Introduction to Probability and Statistics
Fall 2018: Indiana University, M343  Introduction to Differential Equations with Applications 1 (two sections)
