fluid-structure interaction

scientific coordinator: Filippo Gazzola

The goal is to address key questions concerning the behavior of fluids in interaction with complex structures, like the stability of both the fluid and the structure or optimal position and shape optimization of the structure within the fluid, by theoretical and computer-assisted methods.

Preprints

F. Gazzola, H. C. Grunau, G. Sperone, "A unified approach to the divergence equation and related functional inequalities", preprint arXiv:2608.25861 [math.AP];
F. Gazzola, "Finite-time blow-up for the forced 2D Navier-Stokes equations", preprint arXiv:2608.18802 [math.AP];
A. Falocchi, A. L. Silvestre, G. Sperone, "On the evolutionary Navier-Stokes equations in distorted pipes under dynamic and energy-stable outflow boundary conditions", preprint arXiv:2608.08841 [math.AP];
A. Agosti, A. Giorgini, "Numerical analysis and coarsening dynamics of the Active Cahn-Hilliard equation", preprint arXiv:2608.07450 [math.NA];
M. Conti, A. Giorgini, G. Ricchi, "Global weak solutions to the Cahn-Hilliard equation with degenerate mobility and singular diffusion", preprint arXiv:2608.06371 [math.AP];
G. P. Galdi, F. Gazzola, "Blow-up and uniqueness of Leray-Hopf solutions to forced Navier-Stokes equations", preprint arXiv:2606.15189 [math.AP];
E. Bocchi, F. Gazzola, A. Hidalgo-Torné, "On spiral steady flows for the Couette-Taylor problem", preprint arXiv:2603.05401 [math.AP];
A. Giorgini, J. He, H. Wu, "On a thermodynamically consistent diffuse-interface model for incompressible two-phase flows with chemotaxis and mass transport", preprint arXiv:2512.22585 [math.AP];
D. Basaric, A. Giorgini, "Global weak solutions to a compressible Navier--Stokes/Cahn--Hilliard system with singular entropy of mixing", preprint arXiv:2506.07835 [math.AP];
A. Falocchi, A. L. Silvestre, G. Sperone, "On the stationary Navier-Stokes equations in distorted pipes under energy-stable outflow boundary conditions", preprint arXiv:2506.07331 [math.AP];
F. Gazzola, M. V. Korobkov, X. Ren, G. Sperone, "The steady Navier-Stokes equations in a system of unbounded channels with sources and sinks", preprint arXiv:2505.14642 [math.AP];
M. Garrione, E. Pastorino,"Stability analysis for a nonlocal asymmetric PDE model related to suspension bridge dynamics", preprint Research Gate.

Publications

2025

M. Conti, P. Galimberti, S. Gatti, A. Giorgini, "New results for the Cahn-Hilliard equation with non-degenerate mobility: well-posedness and longtime behavior", Calc. Var. 64, 87, 2025;
D. Bonheure, G.P. Galdi, F. Gazzola, "Flow-induced Oscillations via Hopf Bifurcation in a Fluid-Solid Interaction Problem", Math. Ann. 392, 4, 4939-4982, 2025;
E. Bocchi, F. Gazzola, "A measure for the stability of structures immersed in a 2D laminar flow", Boll. Unione Mat. Ital. 18, 49-63, 2025;
V. Bianca, E. Bocchi, F. Gazzola, "Equilibrium configurations of a 3D fluid-beam interaction problem", Appl. Math. Optim. 92, 50, 2025;
L. Berselli, A. Falocchi, R. Sannipoli, "On a 3D Stokes eigenvalue problem under Navier slip-with-friction boundary conditions and applications to Navier-Stokes equations", Z. Angew. Math. Phys. 76, 175, 2025;
M. Akil, F. Dell’Oro, G. Fragnelli, V. Régnier and A. Soufyane, "Asymptotic behavior of the equivalent Timoshenko linear beam model used in the analysis of tower buildings", Z. Angew. Math. Phys. 76, 40, 2025;
A. Abbatiello, D. Basaric, N. Chaudhuri, "On a blow-up criterion for the Navier-Stokes-Forurier system under general equations of state", Nonlinear Anal. RWA 84, 104328, 2025;

2024

V. Racic, F. Gazzola, "Model of coordinated crowd dynamics", J. Phys.: Conf. Ser. 2647, 252015; 2024.
A. Giorgini, "On the separation property and the global attractor for the nonlocal Cahn-Hilliard equation in three dimensions", J. Evol. Equ. 24, 21, 2024;
F. Gazzola, V. Pata, C. Patriarca, "Attractors for a fluid-structure interaction problem in a time-dependent phase space", J. Funct. Anal. 286, 110199, 2024;
M. Garrione, E. Pastorino, "Long-Time Behaviour for Solutions of Systems of PDEs Modelling Suspension Bridges", in H. Beirão da Veiga, F. Minhós, N. Van Goethem, L. Sanchez Rodrigues (eds.), Nonlinear Differential Equations and Applications, CIM Series in Mathematical Sciences 7, Springer, 2024;
R. Feola, F. Giuliani, F. Iandoli, J.E. Massetti, "Local well posedness for a system of quasilinear PDEs modelling suspension bridges", Nonlinear Anal. 240, 113442, 2024;
A. Falocchi, F. Gazzola, “The Kernel of the Strain Tensor for Solenoidal Vector Fields with Homogeneous Normal Trace", in H. Beirão da Veiga, F. Minhós, N. Van Goethem, L. Sanchez Rodrigues (eds.), Nonlinear Differential Equations and Applications, CIM Series in Mathematical Sciences 7, Springer, 2024;
D. Bonheure, G.P. Galdi, F. Gazzola, "Stability of equilibria and bifurcations for a fluid-solid interaction problem", J. Differential Equations 408, 324-367, 2024;
G. Bevilacqua, A. Giorgini, "Global Solutions for Two-Phase Complex Fluids with Quadratic Anchoring in Soft Matter Physics", SIAM J. Math. Anal. 56, 6057-6120, 2024;
E. Berchio, A. Falocchi, C. Patriarca, "On the long-time behaviour of solutions to unforced evolution Navier–Stokes equations under Navier boundary conditions", Nonlinear Anal. RWA 79, 104102, 2024;
E. Berchio, D. Bonheure, G.P. Galdi, F. Gazzola, S. Perotto, "Equilibrium Configurations of a Symmetric Body Immersed in a Stationary Navier–Stokes Flow in a Planar Channel", SIAM J. Math. Anal. 56, 3759-3801, 2024;
D. Basaric, N. Chaudhuri, "Low Mach number limit on perforated domains for the evolutionary Navier–Stokes–Fourier system", Nonlinearity 37, 065008, 2024;
P. Baldi, F. Giuliani, M. Guardia, E. Haus, "Effective chaos for the Kirchhoff equation on tori", Ann. Inst. H. Poincaré C Anal. Non Linéaire online (2024);

2023

G. Sperone, “Homogenization of the steady-state Navier Stokes equations with prescribed flux rate or pressure drop in a perforated pipe”, J. Differential Equations 375, 653-681, 2023.