Roberta Bianchini
Researcher, IAC, National Research Council - CNR

My main interests are partial differential equations, Fourier analysis and numerical analysis, with special enthusiasm in fluid-dynamics problems, where a combination of those succeeds. Here are my Google Scholar footprints. Most of my papers are also available on the arXiv preprint server and some of them on HAL. A few of them are also on ResearchGate.

Preprints

  1. R. Bianchini, V. Duchene, On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity. https://arxiv.org/abs/2206.01058

  2. R. Bianchini, T. Paul, Reflection of internal gravity waves in the form of quasi-axisymmetric beams. https://arxiv.org/abs/2205.06074

  3. 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

  4. J. Bedrossian, R. Bianchini, M. Coti Zelati, M. Dolce, Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations. https://arxiv.org/pdf/2103.13713v1.pdf

Published or accepted by a journal

  1. R. Bianchini, R. Natalini, Nonresonant bilinear forms for partially dissipative hyperbolic systems violating the Shizuta-Kawashima condition.
    Journal of Evolution Equations , in press. Available at https://arxiv.org/abs/1906.02767

  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, 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

  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, in press. Available at https://arxiv.org/abs/2005.09058

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. R. Bianchini, L. Gosse, E. Zuazua, A two-dimensional ''flea on the elephant" phenomenon and its numerical visualization,
    Multiscale Modeling & Simulation 17 (1)(2019), 137-166. https://hal.archives-ouvertes.fr/hal-01935261

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

    17. Expository papers and proceedings

    1. 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

    2. 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