Related papers: The dissipative linear Boltzmann equation for hard…
We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex…
Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…
We study, globaly in time, the velocity distribution $f(v,t)$ of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant external electric field $E$. The density $f$ satisfies a…
We start with some global Maxwellian function $M$, which is a stationary solution (with the constant total density $\rho$) of the Boltzmann equation, and we denote the number of the corresponding space variables by $n$. The notion of…
On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One…
In this paper, we prove some a priori stability estimates (in weighted Sobolev spaces) for the spatially homogeneous Boltzmann equation without angular cutoff (covering every physical collision kernels). These estimates are conditioned to…
The Vicsek-BGK equation is a kinetic model for alignment of particles moving with constant speed between stochastic reorientation events with sampling from a von Mises distribution. The spatially homogeneous model shows a steady state…
We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion…
This paper is devoted to the study of the dynamics of charged particles in a weakly inhomogeneous dilute gas. More precisely, we consider the existence of unique global in time classical solutions for the Vlasov-MaxwellBoltzmann system and…
An explicit estimate is derived for Kac's mean-field model of colliding hard spheres, which compares, in a Wasserstein distance, the empirical velocity distributions for two versions of the model based on different numbers of particles. For…
In this article the static Einstein-Vlasov-Maxwell system is considered in spherical symmetry. This system describes an ensemble of charged particles interacting by general relativistic gravity and Coulomb forces. First, a proof for local…
In this work we prove global stability for the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse power intermolecular potentials, $r^{-(p-1)}$ with $p>2$. This completes…
Cold atoms in dissipative optical lattices have long been known to exhibit anomalous kinetics due to an effective nonlinear friction force. Here we show that confining the spatial motion of the atoms will lead to an anomalous…
An impurity particle coupling to its host fluid via inelastic hard sphere collisions is considered. It is shown that the exact equation for its distribution function can be mapped onto that for an impurity with elastic collisions and an…
We consider a gas of $N$ identical hard spheres in the whole space, and we enforce the Boltzmann-Grad scaling. We may suppose that the particles are essentially independent of each other at some initial time; even so, correlations will be…
The paper is concerned with the spatially homogeneous isotropic Boltzmann equation for Bose-Einstein particles with quantum collision kernel where the interaction potential $\phi({\bf x})$ can be approximately written as the delta function…
We consider a set of identical mobile point-like charges (counter-ions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are…
The paper proves existence of mild solutions to normal discrete velocity Boltzmann equations sin the plane with no pair of colinear interacting velocities, and given ingoing boundary values. A key property is L1 compactness of the…
We consider the rate of convergence of solutions of spatially inhomogenous Boltzmann equations, with hard sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially homogenous static Maxwell velocity…
We consider a stochastic $N$-particle model for the spatially homogeneous Boltzmann evolution and prove its convergence to the associated Boltzmann equation when $N\to \infty$. For any time $T>0$ we bound the distance between the empirical…