Roberta Bianchini

Roberta Bianchini
Italian National Research Council | CNR · Institute for Applied Mathematics "Mauro Picone" IAC

PhD

About

33
Publications
4,469
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
68
Citations
Introduction
I'm a researcher at Istituto per le Applicazioni del Calcolo Mauro Picone, CNR (Rome, Italy). My research focuses on hyperbolic systems and fluid-dynamics models.
Additional affiliations
October 2016 - December 2017
Università Degli Studi Roma Tre
Position
  • Tutor for ''Analisi 1''
November 2014 - December 2017
University of Rome Tor Vergata
Position
  • PhD Student
Education
November 2014 - December 2017
University of Rome Tor Vergata
Field of study
  • Mathematics, Analysis
November 2012 - July 2014
Sapienza University of Rome
Field of study
  • Mathematics, Applied Mathematics
November 2009 - July 2012
Sapienza University of Rome
Field of study
  • Mathematics

Publications

Publications (33)
Article
Full-text available
In the context of hyperbolic systems of balance laws, the Shizuta–Kawashima coupling condition guarantees that all the variables of the system are dissipative even though the system is not totally dissipative. Hence it plays a crucial role in terms of sufficient conditions for the global in time existence of classical solutions. However, it is easy...
Preprint
Full-text available
This article is concerned with the rigorous justification of the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main peculiarity of this work with respect to previous studies is that no (regularizing) viscosity contribution is added to the fluid-dynamics equations and only diffusivity effects...
Preprint
Full-text available
Preservation of the angle of reflection when an internal gravity wave hits a sloping boundary generates a focusing mechanism if the angle between the direction of propagation of the incident wave and the horizontal is close to the slope inclination (near-critical reflection). We establish a rigorous analysis of this phenomenon in two space dimensio...
Preprint
Full-text available
The aim of this work is to make a further step towards the understanding of the near-critical reflection of internal gravity waves from a slope in the more general and realistic context where the size of viscosity $\nu$ and the size of diffusivity $\kappa$ are different. In particular, we provide a systematic characterization of boundary layers (bo...
Article
Full-text available
This article deals with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined with b...
Preprint
Full-text available
We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size $\varepsilon$. Under the classical Miles-Howard stability condition on the Richardson number, we prove that the system experiences a shear-buoyancy instability: the density va...
Preprint
Full-text available
This article is concerned with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined...
Preprint
Full-text available
This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded weak solutions by means of a viscous regularization and refined compensated compactness arguments. Second, we i...
Preprint
Full-text available
We investigate the linear stability of shears near the Couette flow for a class of 2D incompressible stably stratified fluids. Our main result consists of nearly optimal decay rates for perturbations of stationary states whose velocities are monotone shear flows $(U(y),0)$ and have an exponential density profile. In the case of the Couette flow $U(...
Preprint
Full-text available
Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable. This is one of the main features of wave turbulence.
Preprint
Full-text available
To cite this version: Roberta Bianchini, Gigliola Staffilani. Revisitation of a Tartar's result on a semilinear hyperbolic system with null condition. hal-02435530. (2020) Abstract We revisit a method introduced by Tartar for proving global well-posedness of a semilinear hyperbolic system with null quadratic source in one space dimension. A remarka...
Preprint
Full-text available
We provide a framework to extend the relative entropy method to a class of diffusive relaxation systems with discrete velocities. The methodology is detailed in the toy case of the 1D Jin-Xin model under the diffusive scaling, and provides a direct proof of convergence to the limit parabolic equation in any interval of time, in the regime where the...
Preprint
Full-text available
We consider a simple example of a partially dissipative hyperbolic system violating the Shizuta-Kawashima condition, i.e. such that some eigendirections do not exhibit dissipation at all. In the space-time resonances framework introduced by Germain, Masmoudi and Shatah, we prove that, when the source term has a Nonresonant Bilinear Form, as propose...
Preprint
Full-text available
Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore the reflection on a sloping boundary cannot follow Descartes' laws, and it is expected to be singular if the sl...
Article
The aim of this paper is to prove the strong convergence of the solutions to a vector-BGK model under the diffusive scaling to the incompressible Navier-Stokes equations on the two-dimensional torus. This result holds in any interval of time [0; T], with T > 0. We also provide the global in time uniform boundedness of the solutions to the approxima...
Preprint
Full-text available
Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore the reflection on a sloping boundary cannot follow Descartes' laws, and it is expected to be singular if the sl...
Article
Full-text available
We present a rigorous convergence result for the smooth solutions to a singular semilinear hyperbolic approximation, a vector BGK model, to the solutions to the incompressible Navier-Stokes equations in Sobolev spaces. Our proof is based on the use of a constant right symmetrizer, weighted with respect to the parameter of the singular pertubation s...
Preprint
Full-text available
The aim of this paper is to prove the strong convergence of the solutions to a vector-BGK model under the diffusive scaling to the incompressible Navier-Stokes equations on the two-dimensional torus. This result holds in any interval of time [0, T ], with T > 0. We also provide the global in time uniform boundedness of the solutions to the approxim...
Presentation
Full-text available
These are the slides corresponding to my Invited Talk at the NumAsp'18 Conference, see https://numasp2018.wordpress.com/
Article
Full-text available
Localization phenomena (sometimes called "flea on the elephant") for the operator L ε = −ε 2 ∆u + p(x)u, p(x) being an unbounded potential, are studied both analytically and numerically, mostly in two space dimensions and within a perturbative framework. Starting from the classical harmonic potential, the effects of various perturbations is retriev...
Article
Full-text available
We provide sharp decay estimates in time in the context of Sobolev spaces, for smooth solutions to the one dimensional Jin-Xin model under the diffusion scaling, which are uniform with respect to the singular parameter of the scaling. This provides convergence to the limit nonlinear parabolic equation both for large time, and for the vanishing sing...
Article
Full-text available
A genuinely two-dimensional discretization of general drift-diffusion (including in-compressible Navier-Stokes) equations is proposed. Its numerical fluxes are derived by computing the radial derivatives of "bubbles" which are deduced from available discrete data by exploiting the stationary Dirichlet-Green function of the convection-diffusion oper...
Article
Full-text available
We propose a model of a density-dependent compressible-incompressible fluid, which is intended as a simplified version of models based on mixture theory as, for instance, those arising in the study of biofilms, tumor growth and vasculogenesis. Though our model is, in some sense, close to the density-dependent incompressible Euler equations, it pres...
Article
Full-text available
In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility constraint, and the gradient of a compressible pressure depending on the volume fractions of some of the diff...
Article
Full-text available
We propose a model of a density-dependent compressible-incompressible fluid, which is intended as a simplified version of models based on mixture theory, as for instance those arising in the study of biofilms, tumor growth, and vasculogenesis. Though our compressible-incompressible model seems to be very close to the density-dependent incompressibl...
Article
Full-text available
In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [4] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in a open neighborhood of the physical parameters, the system is totally dissipative near its unique non vanishing equilibrium...

Network

Cited By

Projects

Projects (9)
Project
Investigate the stability of hydrostatic steady state and the behavior of the fluctuations in different domains and regimes of the involved physical parameters.
Project
Rigorous mathematical study of phenomena of reflection and interaction of internal gravity waves for application in oceanography and in connection with wave turbulence.