★ (2025) R. Bianchini, M.J.Jo, J. Park, S. Wang, Sharp asymptotic stability of the incompressible porous media equation. arXiv:2505.05165 (2025)
★ (2024) C. Balzotti, R. Bianchini, M. Briani, B. Piccoli, Adapting Priority Riemann Solver for GSOM on road networks.arXiv:2412.18560
★ (2024) R. Bianchini, M. Coti Zelati, L. Ertzbischoff, Ill-posedness of the hydrostatic Euler-Boussinesq equations and failure of hydrostatic limit.arXiv:2403.17857
★ Stability, Instability and Blow-up in Incompressible Fluids with Variable Density
★ (2025) R. Bianchini, T. M. Elgindi, Finite-time singularity formation for scalar stretching equations.Nonlinearity, 38. DOI
★ (2025) R. Bianchini, L. Franzoi, R. Montalto, S. Terracina, Large-amplitude quasi-periodic traveling waves in forced rotating fluids.Commun. Math. Phys., 66. DOI
★ (2024) R. Bianchini, T. Paul, Reflection of internal gravity waves in the form of quasi-axisymmetric beams.J. Funct. Anal. 286(1), 110189. DOI
★ (2024) R. Bianchini, L. Hientzsch, F. Iandoli, Strong Ill-Posedness in L∞ of the 2D Boussinesq Equations in Vorticity Form and Application to the 3D Axisymmetric Euler Equations.SIAM J. Math. Anal., 56(5). DOI
★ (2023) J. Bedrossian, R. Bianchini, M. Coti Zelati, M. Dolce, Nonlinear inviscid damping and shear-buoyancy instability in stably stratified fluids near Couette.Comm. Pure Appl. Math. 76(12), 3685–3768. DOI
★ (2022) R. Bianchini, M. Coti Zelati, M. Dolce, Linear inviscid damping for shear flows near Couette in stratified fluids.Indiana Univ. Math. J. 71(4), 1467–1504.
★ (2022) R. Bianchini, G. Orrù, Linear boundary layer analysis in a stably stratified hydrostatic flow.Springer INdAM Series. arXiv
★ (2021) R. Bianchini, A.-L. Dalibard, L. Saint-Raymond, Near-critical reflection of internal waves.Analysis & PDE 14(1), 205–249. DOI
★ Incompressible Porous Media & Damped Boussinesq
★ (2025) R. Bianchini, D. Cordoba, L. Martinez‑Zoroa, Non Existence and Strong Ill-posedness in $H^2$ for the Stable IPM Equation. J. Funct. Anal., in press.arXiv:2410.01297
★ (2024) R. Bianchini, T. Crin-Barat, M. Paicu, Relaxation approximation and asymptotic stability of stratified solutions to the incompressible porous media equation.Arch. Ration. Mech. Anal. 248(2). DOI
★ (2021) R. Bianchini, R. Natalini, Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation.ESAIM: Control, Optimisation and Calculus of Variations 27. DOI
★ Hydrostatic Equations with Variable Density
★ (2024) M. Adim, R. Bianchini, V. Duchêne, Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems C. R. Math.362, 1597–1626. DOI
★ (2024) R. Bianchini, V. Duchêne, On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity. Comm. Partial Differential Equations 49(5–6). DOI
★ Hyperbolic Systems & Congestion Models
★ (2024) R. Bianchini, V. Laheurte, F. Sueur, A new look at the controllability cost of linear evolution systems with a long gaze at localized data.C. R. Math., 363 (2025), pp. 241-266. DOI
★ (2023) F. Ancona, R. Bianchini, C. Perrin, Hard-congestion limit of the p-system in BV setting.ESAIM Proc. Surveys 72, 41–63.
★ (2021) R. Bianchini, C. Perrin, Soft congestion approximation to the one-dimensional constrained Euler equations.Nonlinearity 34(10), 6901. DOI
★ (2022) R. Bianchini, R. Natalini, Nonresonant bilinear forms for partially dissipative hyperbolic systems violating the Shizuta–Kawashima condition. J. Evol. Equations 22(3). DOI
★ (2020) R. Bianchini, G. Staffilani, Revisitation of a Tartar's result on a semilinear hyperbolic system with null condition.Springer UMI Series. arXiv
★ (2020) R. Bianchini, A.-L. Dalibard, One-dimensional turbulence with Burgers.Springer UMI Series. arXiv
★ Vector-Kinetic BGK Approximation
★ (2021) R. Bianchini, Relative entropy in diffusive relaxation for discrete velocities BGK models.Commun. Math. Sci. 19(1). arXiv
★ (2019) R. Bianchini, R. Natalini, Convergence of a vector-BGK approximation for the incompressible Navier-Stokes equations.Kinetic & Related Models 12(1), 133–158. DOI
★ (2019) R. Bianchini, Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations via the relative entropy method.J. Math. Pures Appl. 132, 280–307. DOI
★ (2018) R. Bianchini, Uniform Asymptotic and Convergence Estimates for the Jin--Xin Model Under the Diffusion Scaling. SIAM J. Math. Anal. 50(2), 1877–1899. DOI
★ Well-Balanced Numerical Schemes in 2D
★ (2019) R. Bianchini, L. Gosse, E. Zuazua, A Two-Dimensional “Flea on the Elephant” Phenomenon and its Numerical Visualization.Multiscale Model. Simul. 17(1), 137–166. DOI
★ (2018) R. Bianchini, L. Gosse, A Truly Two-Dimensional Discretization of Drift-Diffusion Equations on Cartesian Grids.SIAM J. Numer. Anal. 56(5), 2845–2870. DOI
★ Multiphase Models for Mixtures
★ (2019) R. Bianchini, R. Natalini, The paradifferential approach to the local well-posedness of some problems in mixture theory in two space dimensions.Commun. Partial Differential Equations 43(7), 1051–1072. DOI
★ (2017) R. Bianchini, R. Natalini, Well-posedness of a model of nonhomogeneous compressible–incompressible fluids. J. Hyperbolic Differ. Equ.14(3), 487–516. DOI
★ (2016) R. Bianchini, R. Natalini, Global existence and asymptotic stability of smooth solutions to a fluid dynamics model of biofilms in one space dimension. J. Math. Anal. Appl. 434, 1909–1923. DOI
★ Expository Papers & Proceedings
★ (2024) R. Bianchini, L. Ertzbischoff, Mathematical insights into hydrostatic modeling of stratified fluids. Communications in Applied and Industrial Mathematics (CAIM) 15(1), 86–105. DOI
★ (2023) R. Bianchini, C. Saffirio, Fluid instabilities, waves and non-equilibrium dynamics of interacting particles: a short overview.Mathematics in Engineering 5(2), 1–5.
★ (2022) R. Bianchini, M. Coti Zelati, M. Dolce, Symmetrization and asymptotic stability in non-homogeneous fluids around stratified shear flows. Séminaire Laurent Schwartz.link
★ (2021) R. Bianchini, R. Natalini, Space-times resonances and weakly dissipative hyperbolic systems. Oberwolfach Reports 11/2021. PDF
