# Boltzmann equation for granular media with thermal force in a weakly inhomogeneous setting

@article{Tristani2013BoltzmannEF, title={Boltzmann equation for granular media with thermal force in a weakly inhomogeneous setting}, author={Isabelle Tristani}, journal={Journal of Functional Analysis}, year={2013}, volume={270}, pages={1922-1970} }

## 26 Citations

### From Boltzmann Equation for Granular Gases to a Modified Navier–Stokes–Fourier System

- MathematicsJournal of Statistical Physics
- 2022

In this paper, we give an overview of the results established in Alonso (http://arxiv.org/org/abs/2008.05173, 2020) which provides the first rigorous derivation of hydrodynamic equations from the…

### Fluid dynamic limit of Boltzmann equation for granular hard--spheres in a nearly elastic regime

- Physics, Mathematics
- 2020

In this paper, we provide the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres with small inelasticity. The hydrodynamic system that we…

### Convergence to self-similarity for ballistic annihilation dynamics

- PhysicsJournal de Mathématiques Pures et Appliquées
- 2020

### Landau Equation for Very Soft and Coulomb Potentials Near Maxwellians

- Mathematics
- 2015

This work deals with the Landau equation for very soft and Coulomb potentials near the associated Maxwellian equilibrium. We first investigate the corresponding linearized operator and develop a…

### Fractional Fokker-Planck Equation with General Confinement Force

- MathematicsSIAM J. Math. Anal.
- 2020

A Fokker-Planck type equation of fractional diffusion with conservative drift has a property of regularization in fractional Sobolev spaces, as well as a gain of integrability and positivity which it uses to obtain polynomial or exponential convergence to equilibrium in weighted Lebesgue spaces.

### Uniqueness and long time asymptotics for the parabolic–parabolic Keller–Segel equation

- Mathematics
- 2014

ABSTRACT The present paper deals with the parabolic–parabolic Keller–Segel equation in the plane in the general framework of weak (or “free energy”) solutions associated to initial data with finite…

### Global well-posedness and exponential stability for the fermion equation in weighted Sobolev spaces

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2021

This work deals with the Cauchy problem and the asymptotic behavior of the solution of the fermion equation in the Sobolev spaces with a polynomial weight in the torus. We first investigate the…

### Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

- Physics
- 2016

We investigate the behavior of granular gases in the limit of small Knudsen number, that is very frequent collisions. We deal with the strongly inelastic case, in one dimension of space and velocity.…

### Exponential convergence for the linear homogeneous Boltzmann equation for hard potentials

- MathematicsAppl. Math. Comput.
- 2018

### Stability for the models of neuronal network and chemotaxis

- Mathematics
- 2017

This thesis is aimed to study some biological models in neuronal network and chemotaxis with the spectral analysis method. In order to deal with the main concerning problems, such as the existence…

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We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the initial datum is a…

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We study the uniqueness and regularity of the steady states of the diffusively driven Boltzmann equation in the physically relevant case where the restitution coefficient depends on the impact…

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We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar…

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We consider a space-homogeneous gas of {\it inelastic hard spheres}, with a {\it diffusive term} representing a random background forcing (in the framework of so-called {\em constant normal…

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We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution…

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This article investigates the long-time behavior of the solutions to the energy-dependent, spatially homogeneous, inelastic Boltzmann equation for hard spheres with and without drift term by introducing new strongly “nonlinear” self-similar variables.

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For the spatially homogeneous Boltzmann equation with hard potentials and Grad's cutoff (e.g. hard spheres), we give quantitative estimates of exponential convergence to equilibrium, and we show that…

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The Cauchy problem for the inelastic Boltzmann equation is studied for small data. Existence and uniqueness of mild and weak solutions is obtained for sufficiently small data that lies in the space…

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We study high-energy asymptotics of the steady velocity distributions for model kinetic equations describing various regimes in dilute granular flows. The main results obtained are integral estimates…

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For a general class of linear collisional kinetic models in the torus, including in particular the linearized Boltzmann equation for hard spheres, the linearized Landau equation with hard and…