相关论文: Measure Valued Solution to the Spatially Homogeneo…
Using relativistic kinetic theory, we study spherically symmetric, static equilibrium configurations of a collisionless Maxwell-Boltzmann gas with non-standard self-interactions, modelled by an effective one--particle force. The resulting…
Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…
The exact nonequilibrium steady state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier…
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…
We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The…
We develop error estimates for the semi-discrete conservative spectral method for the approximation of the elastic and inelastic space homogeneous Boltzmann equation introduced by the authors in \cite{GT09}. In addition we study the long…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
We study the Boltzmann equation near vacuum in anisotropic low-regularity Besov spaces. We establish the global existence and uniqueness of strong solutions with the critical regularity index $2/p$ for $p\in[1,\infty)$ in $\mathbb{R}^3$.…
The notion of distance between a global Maxwellian function and an arbitrary solution $f$ (with the same total density $\rho$ at the fixed moment $t$) of Boltzmann equation is introduced. In this way we essentially generalize the important…
We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient $\alpha\in(0,1)$, under the thermalization induced by a host medium with a fixed Maxwellian distribution and any…
In this paper, we study the global well-posedness of the Boltzmann equation within the $L_{v}^{p}L_{x}^{\infty}$ framework for soft potential models with angular cutoff in a periodic box $\mathbb{T}^3$. By using a time-involved weight…
From a unified vision of vector valued solutions in weighted Banach spaces, this manuscript establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex…
In this paper, we consider the spatially homogeneous Landau equation, which is a variation of the Boltzmann equation in the grazing collision limit. For the Landau equation for hard potentials in the style of Desvillettes-Villani (Comm.…
We prove the existence and uniqueness of global solutions to the Boltzmann equation with non-cutoff soft potentials in the whole space when the initial data is a small perturbation of a Maxwellian with polynomial decay in velocity. Our…
The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to analyze transport properties for monodisperse gas-solid suspensions. The influence of the interstitial gas phase on the dynamics of solid particles is…
We review some recent developments of Grad's approach to solving the Boltzmann equation and creating reduced description. The method of invariant manifold is put forward as a unified principle to establish corrections to Grad's equations. A…
In this work, we study the Cauchy problem for the spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. We prove that this Cauchy problem enjoys Gelfand-Shilov regularizing effect, that means the smoothing…
In this paper we continue the formal analysis of the long-time asymptotics of the homoenergetic solutions for the Boltzmann equation that we began in [18]. They have the form $f\left( x,v,t\right) =g\left(v-L\left( t\right) x,t\right) $…
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…
In this paper, a polyatomic gas with continuous internal energy is considered, allowing for frozen collisions, in which the kinetic energy of the colliding particle pair is conserved, and the internal energy of each particle remains…