Related papers: Compactness of linearized Boltzmann operators for …
In this paper, we investigate a compactness property of the linearized Boltzmann operator in the context of a polyatomic gas whose molecules undergo resonant collisions. The peculiar structure of resonant collision rules allows to tensorize…
The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were…
The linearized Boltzmann collision operator is fundamental in many studies of the Boltzmann equation and its main properties are of substantial importance. The decomposition into a sum of a positive multiplication operator, the collision…
The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for…
At higher altitudes, for high temperature gases, for instance near space shuttles moving at hypersonic speed, not only mechanical collisions are affecting the gas flow, but also chemical reactions have an impact on such hypersonic flows. In…
The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently,…
A general framework for the kinetic modelling of non-relativistic polyatomic gases is proposed,where each particle is characterized both by its velocity and by its internal state, and the Boltzmann collisionoperator involves suitably…
In the following work, we consider the Boltzmann equation that models a polyatomic gas by representing the microscopic internal energy by a continuous variable I. Under some convenient assumptions on the collision cross-section…
This paper reviews results on the scalar Boltzmann equation for a single-component polyatomic gas with continuous internal energy. For the space homogeneous problem, $L^1$-theory is established, for solutions with initial strictly positive…
We consider hard-potential cutoff multi-species Boltzmann operators modeling microscopic binary elastic collisions and bimolecular reversible chemical reactions inside a gaseous mixture. We prove that the spectral gap estimate derived for…
This paper considers a system of Boltzmann equations modelling the mixture of monatomic and polyatomic gases in an $L^{2}-L^{\infty}$ perturbation theory around global modified Maxwellians accounting for the internal energy of the mixture…
The periodic Lorentz gas describes an ensemble of non-interacting point particles in a periodic array of spherical scatterers. We have recently shown that, in the limit of small scatterer density (Boltzmann-Grad limit), the macroscopic…
We investigate the properties of the collision operator associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non-dissipative interactions, the gain…
We consider the existence of steady rarefied flows of polyatomic gas between two parallel condensed phases, where evaporation and condensation processes occur. To this end, we study the existence problem of stationary solutions in a…
In this paper we consider the Boltzmann equation modelling the motion of a polyatomic gas where the integration collision operator in comparison with the classical one involves an additional internal energy variable $I\in\mathbb{R}_+$ and a…
This minicourse contains a description of recent results on the modelling of rarefied gases in weakly non equilibrium regimes, and the numerical methods used to approximate the resulting equations. Therefore this work focuses on BGK type…
A granular gas is a collection of macroscopic particles that interact through energy-dissipating collisions, also known as inelastic collisions. This inelasticity is characterized by a collision mechanics in which mass and momentum are…
We present recent results [4, 28, 29] about the quantitative study of the linearized Boltzmann collision operator, and its application to the study of the trend to equilibrium for the spatially homogeneous Boltzmann equation for hard…
We consider generalizations of kinetic granular gas models given by Boltzmann equations of Maxwell type. These type of models for non-linear elastic or inelastic interactions, have many applications in physics, dynamics of granular gases,…
The Boltzmann equation is essential for gas thermodynamics,as it models how the molecular density distribution $F(t,x,v)$ changes over time. However, existing research primarily focuses on the single species Boltzmann equation, while…