List of publications

Preprints

  1. R. Bianchini, D. Cordoba, L. Martinez-Zoroa, Non Existence and Strong Ill-posedness in $H^2$ for the Stable IPM Equation. arxiv:2410.01297 (2024)
  2. R. Bianchini, T. M. Elgindi, Finite-time singularity formation for scalar stretching equations. arxiv:2407.16450 (2024)
  3. R. Bianchini, L. Franzoi, R. Montalto, S. Terracina, Large amplitude quasi-periodic traveling waves in two dimensional forced rotating fluids. arxiv:2406.07099 (2024)
  4. R. Bianchini, M. Coti Zelati, L. Ertzbischoff, Ill-posedness of the hydrostatic Euler-Boussinesq equations and failure of hydrostatic limit. arXiv:2403.17857 (2024)

  5. R. Bianchini, V. Laheurte, F. Sueur, A new look at the controllability cost of linear evolution systems with a long gaze at localized data. arXiv:2401.07285 (2024)

     

Published or accepted by a journal

* Nonhomogeneous hydrostatic equations 

  1. M. Adim, R. Bianchini, V. Duchene, Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems. Comptes Rendus Mathematique, in press. http://arxiv.org/abs/2405.14164, 2024
  2. R. Bianchini, V. Duchene, On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity. Communications Partial Diff Eqs Volume 49 Issue 5-6 (2024). https://arxiv.org/abs/2206.01058 

* Stratified fluids, Boussinesq equations, inviscid damping and internal gravity waves

  1. R. Bianchini, L.Hientzsch, F. Iandoli, Strong ill-posedness in W1,∞ of the 2d stably stratified Boussinesq equations and application to the 3d axisymmetric Euler Equations. SIAM Journal on Mathematical Analysis, 56(5) (2024) 
  2. R. Bianchini, T. Paul, Reflection of internal gravity waves in the form of quasi-axisymmetric beams. Journal of Functional Analysis 286 (1), 110189 (2024)
  3. J. Bedrossian, R. Bianchini, M. Coti Zelati, M. Dolce, Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations.  Communications on Pure and Applied Mathematics 76 (12), 3685-3768 (2023). Available at https://arxiv.org/pdf/2103.13713v1.pdf 
  4. R. Bianchini, M. Coti Zelati, M. Dolce, Linear inviscid damping for shear flows near Couette in the 2D stably stratified regime, 
    Indiana University Mathematics Journal, 2022, 71(4), pp. 1467–1504. Available at https://arxiv.org/abs/2005.09058
  5. R. Bianchini, A.-L. Dalibard, L. Saint-Raymond, Near-critical reflection of internal waves, 
    preprint arXiv:1902.06669 (2019), Analysis & PDE 14 (1)(2021), 205-249. https://arxiv.org/abs/1902.06669
  6. R. Bianchini, G. Orrù, Linear boundary layer analysis of the near-critical reflection of internal gravity waves with different sizes of viscosity and diffusivity. https://arxiv.org/pdf/2202.10802.pdf (2022). Springer UMI INdAM Series.
  7. R. Bianchini, R. Natalini, Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation.
    ESAIM:COCV 27 (2021) 43 . Available at https://arxiv.org/pdf/2009.01578.pdf
  8. R. Bianchini, A.-L. Dalibard, One-dimensional turbulence with Burgers, Fluid Dynamics, Dispersive Perturbations and Quantum Fluids, Springer UMI Series, in press. Available at https://arxiv.org/abs/2004.02825

* Incompressible Porous Media (IPM) equation

  1. R. Bianchini, T. Crin-Barat, M. Paicu, Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation. Archive for Rational Mechanics and Analysis 248 (2) (2024)

* Hyperbolic systems and congestion models

  1. F. Ancona, R. Bianchini, C. Perrin, Hard-congestion limit of the p-system in the BV setting. ESAIM Proceedings and Surveys 72 (2023) 41-63. 
  2. R. Bianchini, C. Perrin, Soft congestion approximation to the one-dimensional constrained Euler equations. Nonlinearity 34(10) 6901 (2021) . Available at https://arxiv.org/abs/2005.13214
  3. R. Bianchini, R. Natalini, Nonresonant bilinear forms for partially dissipative hyperbolic systems violating the Shizuta-Kawashima condition. 
    Journal of Evolution Equations  22 (3), 1-41. Available at https://arxiv.org/abs/1906.02767
  4. R. Bianchini, G. Staffilani, Revisitation of a Tartar's result on a semilinear hyperbolic system with null condition, Fluid Dynamics, Dispersive Perturbations and Quantum Fluids, Springer UMI Series, in press. Available at https://arxiv.org/abs/2001.03688

* Vector-kinetic BGK approximation to fluid models

  1. R. Bianchini, Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations, Journal de Mathématiques Pures et Appliquées 132 (2019), 280-307. https://arxiv.org/abs/1807.04044
  2. R. Bianchini, Relative entropy in diffusive relaxation for a class of discrete velocities BGK models, 
    preprint arXiv:1912.10988 (2019), Communications in Mathematical Sciences, 19 (1) (2021), 39-54. https://arxiv.org/abs/1912.10988
  3. R. Bianchini, R. Natalini, Convergence of a vector-BGK approximation for the incompressible Navier-Stoker equations, Kinetic and Related Models 12 (1) (2019) , 133-158. https://arxiv.org/abs/1705.04026
  4. R. Bianchini, Uniform asymptotic and convergence estimates for the Jin-Xin model under the diffusion scaling, SIAM Journal on Mathematical Analysis 50 (2) (2018), 1877-1899. https://arxiv.org/abs/1710.05385

* Well-balanced numerical schemes for PDEs in two dimensional space

  1. R. Bianchini, L. Gosse, E. Zuazua, A two-dimensional ''flea on the elephant" phenomenon and its numerical visualization, SIAM Multiscale Modeling & Simulation 17 (1)(2019), 137-166. https://hal.archives-ouvertes.fr/hal-01935261
  2. R. Bianchini, L. Gosse, A ''truly-two dimensional'' discretization of drift-diffusion equations on Cartesian grid, SIAM Numerical Analysis 56 (5)(2018), 2845-2870. https://hal.archives-ouvertes.fr/hal-02012706

* Multiphase models for mixtures

  1. R. Bianchini, R. Natalini, The paradifferential approach to the local well-posedness of some problems in mixture theory, Communications Partial Diff. Eqs. 43 (7)(2019), 1051-1072. https://doi.org/10.1080/03605302.2018.1499775
  2. R. Bianchini, R. Natalini, Well-posedness of a model of nonhomogeneous compressible-incompressible fluids, J. Hyp. Diff. Eq. 14 (3) (2017), 487-516. https://doi.org/10.1142/S0219891617500163
  3. 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 (2016), 1909-1923. https://doi.org/10.1016/j.jmaa.2015.10.014

Expository papers and proceedings

  1. R. Bianchini, L. Ertzbischoff, Mathematical Insights into Hydrostatic Modeling of Stratified Fluids, Communications in Applied and Industrial Mathematics (CAIM) 15 (1), 2024, 86–105
  2. R. Bianchini, M. Coti Zelati, M. Dolce, Symmetrization and asymptotic stability in non-homogeneous fluids around stratified shear flows, Séminaire Laurent Schwartz 2022. http://arxiv.org/abs/2309.12738
  3. R. Bianchini, C. Saffirio, Fluid instabilities, waves and non-equilibrium dynamics of interacting particles: a short overview. Mathematics in Engineering, 2023, 5(2): 1-5 (introduction to a special issue) https://www.aimspress.com/article/10.3934/mine.2023033
  4. R. Bianchini, (with R. Natalini), Space-times resonances and weakly dissipative hyperbolic systems. Oberwolfach Report 11/2021, Hyperbolic balance laws https://publications.mfo.de/bitstream/handle/mfo/3852/OWR_2021_11.pdf?sequence=4&isAllowed=y

 

Link
https://www.iac.cnr.it/personale/roberta-bianchini