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Andrea Giorgini


RTDb (Assistant Professor)
Dipartimento di Matematica
Politecnico di Milano
andrea.giorgini(at)polimi.it
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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.
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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
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    Upcoming Events

    • XI Giornata di Studio Politecnico di Milano - Università di Pavia -- Equazioni Differenziali e Calcolo delle Variazioni
      Politecnico di Milano, October 26, 2023
    • Christmas Workshop on Fluid Dynamics
      Politecnico di Milano, December 19-21, 2023
    • INdAM Workshop Cahn–Hilliard and Allen–Cahn equations in bio-medicine
      Politecnico di Milano, February 22, 2024
    • CIME School Diffuse Interface method in Continuum Mechanics: analysis, singular limits and algorithms
      Cetraro, July 8-12, 2024

    Preprints

    • On the separation property and the global attractor for the nonlocal Cahn-Hilliard equation in three dimensions
      A. Giorgini
      arXiv:2303.06013, 2023
    • Global Solutions for Two-Phase Complex Fluids with Quadratic Anchoring in Soft Matter Physics
      G. Bevilacqua & A. Giorgini
      arXiv:2302.07196, 2023

    Publications

    1. 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.
    2. 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.
    3. Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities
      H. Abels, H. Garcke & A. Giorgini
      Mathematische Annalen. DOI: 10.1007/s00208-023-02670-2 arXiv:2209.10836, 2022
    4. 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).
    5. 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.
    6. On the mass-conserving Allen-Cahn approximation for incompressible binary fluids
      A. Giorgini, M. Grasselli & H. Wu
      Journal of Functional Analysis 283 (2022), 109631.
    7. 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.
    8. 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.
    9. 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.
    10. 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
    11. 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)
    12. 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.
    13. 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
    14. Well-posedness of a diffuse interface model for Hele-Shaw flows
      A. Giorgini
      Journal of Mathematical Fluid Mechanics 22, 5 (2020)
    15. Well-posedness for the Brinkman-Cahn-Hilliard system with unmatched viscosities
      M. Conti & A. Giorgini
      Journal of Differential Equations 268 (2020), 6350-6384
    16. 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
    17. The nonlocal Cahn-Hilliard-Hele-Shaw system with logarithmic potential
      F. Della Porta, A. Giorgini & M. Grasselli
      Nonlinearity 31 (2018), 4851-4881
    18. 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
    19. 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
    20. 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
    21. 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
    22. Phase-field crystal equation with memory
      M. Conti, A. Giorgini & M. Grasselli
      Journal of Mathematical Analysis and Applications 436 (2016), 1297-1331
    23. 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)
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