Flower

Andrea Giorgini


Associate Professor in Mathematical Analysis
Dipartimento di Matematica
Politecnico di Milano
andrea.giorgini(at)polimi.it
Flower

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 two-phase fluid mixtures with different densities, complex internal microstructures and driven by the surface tension.
Flower
My main research directions are:

  • Navier-Stokes-Cahn-Hilliard systems
  • Regularity and separation property for Allen-Cahn and Cahn-Hilliard equations
  • Hele-Shaw and porous media flows with applications to tumor growth dynamics
  • Nonlocal models for long-range particle interactions
  • Multiphysics of complex fluids with applications in Soft Matter and Biology




    Membro del gruppo di ricerca Analysis@PoliMI
    Linea di ricerca: Evolution PDEs, ODEs and dynamical systems
    • Flower

    Upcoming Events

    • The 14th AIMS CONFERENCE on Dynamical Systems, Differential Equations and Applications
      Special Session 10 Analysis of diffuse and sharp interface models
      Abu Dhabi, December 16-20, 2024
    • Fluids@PoliMi
      Politecnico di Milano, January 8-10, 2025

    Preprints

    • New results for the Cahn-Hilliard equation with non-degenerate mobility: well-posedness and longtime behavior
      M. Conti, P. Galimberti, S. Gatti, A. Giorgini
      arXiv:2410.22234 (2024).

    Publications

    1. Global Solutions for Two-Phase Complex Fluids with Quadratic Anchoring in Soft Matter Physics
      G. Bevilacqua & A. Giorgini
      SIAM Journal on Mathematical Analysis 56 (2024), 6057-6120.
    2. On the separation property and the global attractor for the nonlocal Cahn-Hilliard equation in three dimensions
      A. Giorgini
      Journal of Evolution Equations 24, 21 (2024).
    3. Existence and regularity of strong solutions to a nonhomogeneous Kelvin-Voigt-Cahn-Hilliard system
      A. Giorgini, A. Ndongmo Ngana, T. Tachim Medjo & R. Temam
      Journal of Differential Equations 372 (2023), 612-656.
    4. Global well-posedness and convergence to equilibrium for the Abels-Garcke-Grün model with nonlocal free energy
      C.G. Gal, A. Giorgini, M. Grasselli & A. Poiatti
      Journal de Mathématiques Pure et Appliquées 178 (2023), 46-109.
    5. Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities
      H. Abels, H. Garcke & A. Giorgini
      Mathematische Annalen 389 (2024), 1267-1321.
    6. Two-phase flows with bulk-surface interaction: thermodynamically consistent Navier-Stokes-Cahn-Hilliard models with dynamic boundary conditions
      A. Giorgini & P. Knopf
      Journal of Mathematical Fluid Mechanics 25, 65 (2023).
    7. The separation property for 2D Cahn-Hilliard equations: Local, nonlocal, and fractional energy cases
      C.G. Gal, A. Giorgini & M. Grasselli
      Discrete & Continuous Dynamical Systems 43:6 (2023), 2270-2304.
    8. On the mass-conserving Allen-Cahn approximation for incompressible binary fluids
      A. Giorgini, M. Grasselli & H. Wu
      Journal of Functional Analysis 283 (2022), 109631.
    9. Existence and stability of strong solutions to the Abels-Garcke-Grün model in three dimensions
      A. Giorgini
      Interfaces and Free Boundaries 24 (2022), no.4, 565-608.
    10. Continuous data assimilation for the 3D Ladyzhenskaya model: analysis and computations
      Y. Cao, A. Giorgini, M. Jolly & A. Pakzad
      Nonlinear Analysis: Real World Applications 68 (2022), 103659.
    11. Attractors for the Navier-Stokes-Cahn-Hilliard system
      A. Giorgini & R. Temam
      Discrete & Continuous Dynamical Systems - S 15 (2022), 2249-2274. Issue on Mathematics, Models \& Applications: Dedicated to Professor Maurizio Grasselli, on the Occasion of His 60th Birthday.
    12. On the existence of strong solutions to the Cahn-Hilliard-Darcy system with mass source
      A. Giorgini, K.F. Lam, E. Rocca & G. Schimperna
      SIAM Journal on Mathematical Analysis 54 (2022), 737-767
    13. Well-posedness of the two-dimensional Abels-Garcke-Grün model for two-phase flows with unmatched densities
      A. Giorgini
      Calculus of Variations and Partial Differential Equations 60, 100 (2021)
    14. The Navier-Stokes-Cahn-Hilliard equations for mildly compressible binary fluid mixtures
      A. Giorgini, R. Temam & X.-T. Vu
      Discrete & Continuous Dynamical Systems - B 26 (2021), 337-366. Special issue for the 20 years anniversary.
    15. Weak and strong solutions to the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system
      A. Giorgini & R. Temam
      Journal de Mathématiques Pure et Appliquées 144 (2020), 194-249
    16. Well-posedness of a diffuse interface model for Hele-Shaw flows
      A. Giorgini
      Journal of Mathematical Fluid Mechanics 22, 5 (2020)
    17. Well-posedness for the Brinkman-Cahn-Hilliard system with unmatched viscosities
      M. Conti & A. Giorgini
      Journal of Differential Equations 268 (2020), 6350-6384
    18. Uniqueness and regularity for the Navier-Stokes-Cahn-Hilliard system
      A. Giorgini, A. Miranville & R. Temam
      SIAM Journal on Mathematical Analysis 51 (2019), 2535-2574
    19. The nonlocal Cahn-Hilliard-Hele-Shaw system with logarithmic potential
      F. Della Porta, A. Giorgini & M. Grasselli
      Nonlinearity 31 (2018), 4851-4881
    20. The Cahn-Hilliard-Hele-Shaw system with singular potential
      A. Giorgini, M. Grasselli & H. Wu
      Annales de l'Institut Henry Poincaré C, Analyse Non Linéaire 35 (2018), 1079-1118
    21. Navier-Stokes-Voigt equations with memory in 3D lacking instantaneous kinematic viscosity
      F. Di Plinio, A. Giorgini, V. Pata & R. Temam
      Journal of Nonlinear Science 28 (2018), 653-686
    22. The nonlocal Cahn-Hilliard equation with singular potential: well-posedness, regularity and strict separation property
      C.G. Gal, A. Giorgini & M. Grasselli
      Journal of Differential Equations 263 (2017), 5253-5297
    23. The Cahn-Hilliard-Oono equation with singular potential
      A. Giorgini, M. Grasselli & A. Miranville
      Mathematical Models and Methods in Applied Sciences 27 (2017), 2485-2510
    24. Phase-field crystal equation with memory
      M. Conti, A. Giorgini & M. Grasselli
      Journal of Mathematical Analysis and Applications 436 (2016), 1297-1331
    25. On the Swift-Hohenberg equation with slow and fast dynamics: well-posedness and long-time behavior
      A. Giorgini
      Communications on Pure and Applied Analysis 15 (2016), 219-241

    Teaching

  • Spring 2023: Politecnico di Milano - Analisi Matematica II per Ingegneria Biomedica
  • Spring 2022: Imperial College London - Advanced Topics in Partial Differential Equations
  • 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)
    • Cookie policy Privacy policy