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;
F. Gazzola, J. Neustupa, G. Sperone, "On the planar Taylor-Couette system and related exterior problems", preprint Research Gate.

Publications

2026

P. Drabek, M. Garrione, M. Zahradnikova, "Traveling fronts for (q,r)-relativistic operators: existence and asymptotic properties", Math. Nachr., e70261; 2026.
A. Giorgini, J. He, H. Wu, "Global weak solutions to a Navier-Stokes-Cahn-Hilliard system with chemotaxis and mass transport: Cross diffusion versus logistic degradation", Math. Models Methods Appl. Sci. 36, 57-110, 2026.
M. Conti, S. Gatti, A. Giorgini, G. Schimperna, "On the Cahn-Hilliard equation with nonlinear diffusion: the non-convex case", J. Funct. Anal. 291, 9, 2026;
E. Bocchi, Á. Castro, F. Gancedo, "Global-in-time estimates for the 2D one-phase Muskat problem with contact points", Commun. Math. Phys. 407, 121, 2026;
L. Bisconti, M. Caggio, F. Dell’Oro, "Vanishing viscosity limit for the compressible Navier-Stokes equations with non-linear density dependent viscosity", J. Math. Fluid Mech. 28, 46, 2026;
E. Berchio, M. Garrione, C. Patriarca, "Spectral optimization of torsional eigenvalues for a nonhomogeneous fish-bone plate with piers", Appl. Math. Optim. 93, 1, 2026;
D. Basaric, F. Oschmann, J. Pan, "Qualitative derivation of a density dependent incompressible Darcy law", Sci. China Math. 69, 2026;
G. Arioli, A. Falocchi, F. Gazzola, "On the epochs of irregularity of Leray-Hopf solutions to Navier-Stokes equations", J. Differential Equations 453, 113887, 2026;
A. Abbatiello, D. Basaric, N. Chaudhuri, E. Feireisl, "Local existence and conditional regularity for the Navier-Stokes-Fourier system driven by inhomogeneous boundary conditions", J. Evol. Equ. 26, 83, 2026;
A. Giorgini, P. Knopf, J. Stange, "Regularity of a bulk-surface Cahn-Hilliard model driven by Leray velocity fields", Nonlinearity 39, 085013, 2026;
G. P. Galdi, F. Gazzola, M. V. Korobkov, X. Ren, G. Sperone, "On the uniqueness and structural stability of Couette-Poiseuille flow in a channel for arbitrary values of the flux", Arch. Rational Mech. Anal. 250, 93, 2026;

2025

C. Patriarca, G. Sperone, "Homogenization of Leray's flux problem for the steady-state Navier-Stokes equations in a multiply-connected planar domain", J. Nonlinear Sci. 35, 111, 2025.
F. Gazzola, E. M. Marchini, "Optimal control for the Moon lander: the classical problem and variants", New Trends and Challenges in Optimization Theory Applied to Space Engineering, P. Cannarsa et al. (eds.), Springer Optimization and Its Applications 221, Springer, 2025;
M. Garrione, F. Zanolin, "Rich Dynamics for a Model Arising in the Study of Suspension Bridges", J. Nonlinear Sci. 35, 11, 2025;
M. Garrione, F. Gazzola, E. Pastorino, "Unpredictable behavior of a partially damped system of PDEs modeling suspension bridges", SIAM J. Math. Anal. 57, 6, 6633-6659, 2025;
M. Garrione, F. Gazzola, E. Pastorino, "Long-term dynamics of Duffing-type equations with applications to suspension bridges", Z. Angew. Math. Phys. 76, 158, 2025;
A. Falocchi, J. Webster, "Analysis of a nonlinear fish-bone model for suspension bridges with rigid hangers in the presence of flow effects", Discrete and Continuous Dynamical Systems 45(7), 2241-2280, 2025;
A. Falocchi, F. Gazzola, "Blow-up of a modified ODEs system arising from the Galerkin approximation of some Navier-Stokes equations", Rend. Istit. Mat. Univ. Trieste 57, 6, 2025;
F. Dell’Oro, L. Liverani, V. Pata, R. Quintanilla, "Global attractors for Moore-Gibson-Thompson thermoelastic extensible beams and Berger plates", Nonlinear Anal. RWA 84, 104298, 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;