6 papers
Non Maxwellian long-time asymptotics for Homoenergetic Boltzmann flows under strong shear
Alessia Nota, Juan J. L. Velázquez
We compute, using matched asymptotic expansions, the long-time asymptotics of homoenergetic solutions to the nonlinear Boltzmann equation, in presence of a shear term, in the hyper…
Asymptotic Velocity Profiles for Homoenergetic Rayleigh-Boltzmann Flows under Dominant Shear
Nicola Miele, Alessia Nota, Juan J. L. Velázquez
In this paper, we study a particular class of solutions to the Rayleigh--Boltzmann equation, known in the nonlinear setting as \emph{homoenergetic solutions}. These solutions take…
Boltzmann-Grad limit for the inelastic Lorentz gas: Part I. Existence, uniqueness, and rigorous derivation via weak convergence
Théophile Dolmaire, Alessia Nota
In this paper we provide a rigorous derivation of the inelastic linear Boltzmann equation, in the Boltzmann-Grad limit, from a dissipative, random, Lorentz gas in arbitrary dimensi…
The global attractor of the inelastic linear Boltzmann equation in a gravity field for Maxwell molecules
Théophile Dolmaire, Nicola Miele, Alessia Nota
In this article we consider the linear inelastic Boltzmann equation in presence of a uniform and fixed gravity field, in the case of Maxwell molecules. We first obtain a well-posed…
Homoenergetic solutions for the Rayleigh-Boltzmann equation: existence of a stationary non-equilibrium solution
Nicola Miele, Alessia Nota, Juan J. L. Velázquez
In this paper we consider a particular class of solutions of the linear Boltzmann-Rayleigh equation, known in the nonlinear setting as Homoenergetic solutions. These solutions desc…
Diffusion Limit of the Low-Density Magnetic Lorentz Gas
Alessia Nota, Dominik Nowak, Chiara Saffirio
We consider the magnetic Lorentz gas proposed by Bobylev et al. [4], which describes a point particle moving in a random distribution of hard-disk obstacles in under…