List of publications

Selected Publications

(2025) R. Bianchini, T. M. Elgindi, Finite-time singularity formation for scalar stretching equations. Nonlinearity, 38 (2025).

(2025) R. Bianchini, A. Maspero, S. Pasquali, Instabilities of internal gravity waves in the two-dimensional Boussinesq system. SIAM Journal on Mathematical Analysis, to appear.

(2025) R. Bianchini, M. Coti Zelati, L. Ertzbischoff, Ill-posedness of the hydrostatic Euler-Boussinesq equations and failure of hydrostatic limit. Communications in Mathematical Physics, 406, 254 (2025).

(2025) R. Bianchini, D. Córdoba, L. Martínez-Zoroa, Non-existence and strong ill-posedness in $H^2$ for the stable IPM equation. Journal of Functional Analysis, 289(9), 111097 (2025).

(2024) R. Bianchini, L. Hientzsch, F. Iandoli, Strong ill-posedness in $L^\infty$ of the 2D Boussinesq equations in vorticity form and application to the 3D axisymmetric Euler equations. SIAM Journal on Mathematical Analysis, 56(5) (2024).

(2023) J. Bedrossian, R. Bianchini, M. Coti Zelati, M. Dolce, Nonlinear inviscid damping and shear-buoyancy instability in stably stratified fluids near Couette. Communications on Pure and Applied Mathematics, 76(12), 3685--3768 (2023).

(2021) R. Bianchini, A.-L. Dalibard, L. Saint-Raymond, Near-critical reflection of internal waves. Analysis & PDE, 14(1), 205--249 (2021).

(2019) R. Bianchini, Strong convergence of a vector-BGK model to the incompressible Navier--Stokes equations via the relative entropy method. Journal de Mathématiques Pures et Appliquées, 132, 280--307 (2019).

Preprints

  1. (2025) R. Bianchini, M. J. Jo, J. Park, S. Wang, Sharp asymptotic stability of the incompressible porous media equation. arXiv:2505.05165.

Incompressible and Stratified Fluids

  1. (2025) R. Bianchini, A. Maspero, S. Pasquali, Instabilities of internal gravity waves in the two-dimensional Boussinesq system. SIAM Journal on Mathematical Analysis, to appear.
  2. (2025) R. Bianchini, T. M. Elgindi, Finite-time singularity formation for scalar stretching equations. Nonlinearity, 38 (2025).
  3. (2025) R. Bianchini, L. Franzoi, R. Montalto, S. Terracina, Large-amplitude quasi-periodic traveling waves in forced rotating fluids. Communications in Mathematical Physics, 406 (2025).
  4. (2024) R. Bianchini, T. Paul, Reflection of internal gravity waves in the form of quasi-axisymmetric beams. Journal of Functional Analysis, 286(1), 110189 (2024).
  5. (2024) R. Bianchini, L. Hientzsch, F. Iandoli, Strong ill-posedness in $L^\infty$ of the 2D Boussinesq equations in vorticity form and application to the 3D axisymmetric Euler equations. SIAM Journal on Mathematical Analysis, 56(5) (2024).
  6. (2023) J. Bedrossian, R. Bianchini, M. Coti Zelati, M. Dolce, Nonlinear inviscid damping and shear-buoyancy instability in stably stratified fluids near Couette. Communications on Pure and Applied Mathematics, 76(12), 3685--3768 (2023).
  7. (2022) R. Bianchini, M. Coti Zelati, M. Dolce, Linear inviscid damping for shear flows near Couette in stratified fluids. Indiana University Mathematics Journal, 71(4), 1467--1504 (2022).
  8. (2021) R. Bianchini, G. Orrù, Linear Boundary Layer Analysis of the Near-Critical Reflection of Internal Gravity Waves with Different Sizes of Viscosity and Diffusivity. Springer INdAM Series, 63, 1--22 (2025).
  9. (2021) R. Bianchini, A.-L. Dalibard, L. Saint-Raymond, Near-critical reflection of internal waves. Analysis & PDE, 14(1), 205--249 (2021).

Incompressible Porous Media and Related Models

  1. (2025) R. Bianchini, D. Córdoba, L. Martínez-Zoroa, Non-existence and strong ill-posedness in $H^2$ for the stable IPM equation. Journal of Functional Analysis, 289(9), 111097 (2025).
  2. (2024) R. Bianchini, T. Crin-Barat, M. Paicu, Relaxation approximation and asymptotic stability of stratified solutions to the incompressible porous media equation. Archive for Rational Mechanics and Analysis, 248(2) (2024).
  3. (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 (2021).

Hydrostatic and Shallow-Water Models

  1. (2025) R. Bianchini, M. Coti Zelati, L. Ertzbischoff, Ill-posedness of the hydrostatic Euler-Boussinesq equations and failure of hydrostatic limit. Communications in Mathematical Physics, 406, 254 (2025).
  2. (2024) M. Adim, R. Bianchini, V. Duchêne, Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems. Comptes Rendus. Mathématique, 362, 1597--1626 (2024).
  3. (2024) R. Bianchini, V. Duchêne, On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity. Communications in Partial Differential Equations, 49(5--6) (2024).

Hyperbolic Systems, Conservation Laws, and Traffic Models

  1. (2025) C. Balzotti, R. Bianchini, M. Briani, B. Piccoli, Adapting priority Riemann solver for GSOM on road networks. Communications in Mathematical Sciences, 23 (2025).
  2. (2025) R. Bianchini, V. Laheurte, F. Sueur, A new look at the controllability cost of linear evolution systems with a long gaze at localized data. Comptes Rendus. Mathématique, 363, 241--266 (2025).
  3. (2023) F. Ancona, R. Bianchini, C. Perrin, Hard-congestion limit of the p-system in BV setting. ESAIM Proceedings and Surveys, 72, 41--63 (2023).
  4. (2022) R. Bianchini, R. Natalini, Nonresonant bilinear forms for partially dissipative hyperbolic systems violating the Shizuta--Kawashima condition. Journal of Evolution Equations, 22(3) (2022).
  5. (2021) R. Bianchini, C. Perrin, Soft congestion approximation to the one-dimensional constrained Euler equations. Nonlinearity, 34(10), 6901 (2021).
  6. (2020) R. Bianchini, G. Staffilani, Revisitation of a Tartar's result on a semilinear hyperbolic system with null condition. Springer UMI Series (2020).
  7. (2020) R. Bianchini, A.-L. Dalibard, One-dimensional turbulence with Burgers. Springer UMI Series (2020).

Kinetic Models, Relaxation, and Relative Entropy

  1. (2021) R. Bianchini, Relative entropy in diffusive relaxation for discrete velocities BGK models. Communications in Mathematical Sciences, 19(1) (2021).
  2. (2019) R. Bianchini, R. Natalini, Convergence of a vector-BGK approximation for the incompressible Navier--Stokes equations. Kinetic and Related Models, 12(1), 133--158 (2019).
  3. (2019) R. Bianchini, Strong convergence of a vector-BGK model to the incompressible Navier--Stokes equations via the relative entropy method. Journal de Mathématiques Pures et Appliquées, 132, 280--307 (2019).
  4. (2018) R. Bianchini, Uniform asymptotic and convergence estimates for the Jin--Xin model under the diffusion scaling. SIAM Journal on Mathematical Analysis, 50(2), 1877--1899 (2018).

Numerical Methods

  1. (2019) R. Bianchini, L. Gosse, E. Zuazua, A two-dimensional ``Flea on the Elephant'' phenomenon and its numerical visualization. Multiscale Modeling & Simulation, 17(1), 137--166 (2019).
  2. (2018) R. Bianchini, L. Gosse, A truly two-dimensional discretization of drift-diffusion equations on Cartesian grids. SIAM Journal on Numerical Analysis, 56(5), 2845--2870 (2018).

Multiphase and Mixture Models

  1. (2019) R. Bianchini, R. Natalini, The paradifferential approach to the local well-posedness of some problems in mixture theory in two space dimensions. Communications in Partial Differential Equations, 43(7), 1051--1072 (2018).
  2. (2017) R. Bianchini, R. Natalini, Well-posedness of a model of nonhomogeneous compressible--incompressible fluids. Journal of Hyperbolic Differential Equations, 14(3), 487--516 (2017).
  3. (2016) R. Bianchini, R. Natalini, Global existence and asymptotic stability of smooth solutions to a fluid dynamics model of biofilms in one space dimension. Journal of Mathematical Analysis and Applications, 434, 1909--1923 (2016).

Expository Papers and Proceedings

  1. (2024) R. Bianchini, L. Ertzbischoff, Mathematical insights into hydrostatic modeling of stratified fluids. Communications in Applied and Industrial Mathematics, 15(1), 86--105 (2024).
  2. (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 (2023).
  3. (2022) R. Bianchini, M. Coti Zelati, M. Dolce, Symmetrization and asymptotic stability in non-homogeneous fluids around stratified shear flows. Séminaire Laurent Schwartz -- EDP et applications (2022).
  4. (2021) R. Bianchini, R. Natalini, Space-times resonances and weakly dissipative hyperbolic systems. Oberwolfach Reports, 11/2021 (2021).
Link
https://www.iac.cnr.it/personale/roberta-bianchini