相关论文: On the Boltzmann-Grad Limit for the classical hard…

A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions…

This paper investigates the well-posedness of the inhomogeneous Boltzmann and Landau equations in critical function spaces, a fundamental open problem in kinetic theory. We develop a new analytical framework to establish local…

This manuscript focus on an extensive survey with new techniques on the problem of solving the Boltzmann flow by bringing a unified approach to the Cauchy problem to homogeneous kinetic equations with Boltzmann-like collision operators…

We will revisit the classical questions of understanding the statistics of various deterministic dynamics of $N$ hard spheres of diameter $\varepsilon$ with random initial data in the Boltzmann-Grad scaling as $\varepsilon$ tends to zero…

In two recent articles Salazar and Brenig question the validity of kinetic theory for granular gases and fluids, on the based of a supposedly exact hierarchy of coupled equations for the velocity moments, which the authors derive from the…

In this paper we study the kinetic theory of many-particle astrophysical systems and we present a consistent version of the collisionless Boltzmann equation in the 1PN approximation. We argue that the equation presented by Rezania and…

In this work we present several quantitative results of convergence to equilibrium for the linear Boltzmann operator with soft potentials under Grad's angular cutoff assumption. This is done by an adaptation of the famous entropy method and…

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 dimensions d $\geq$ 2. Specifically, we consider a microscopic…

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…

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

We present a derivation of the mechanics of isothermal gas spheres directly from the Vlasov--Poisson equation. By extremising the Boltzmann entropy, we obtain the Maxwell--Boltzmann distribution for a self-gravitating isothermal Newtonian…

In this paper the problem is posed of determining the physically-meaningful asymptotic orderings holding for the statistical description of a large $N-$body system of hard spheres,\textit{ i.e.,} formed by $N\equiv\frac{1}{\varepsilon}…

In spite of the large number of papers appeared in the past which are devoted to the lattice Boltzmann (LB) methods, basic aspects of the theory still remain unchallenged. An unsolved theoretical issue is related to the construction of a…

Consider the steady Boltzmann equation with slab symmetry for a monatomic, hard sphere gas in a half space. At the boundary of the half space, it is assumed that the gas is in contact with its condensed phase. The present paper discusses…

We establish the hydrodynamic limit of the one-dimensional Boltzmann equation with hard-sphere collisions toward Riemann solutions of the compressible Euler system. The Riemann solutions covered by our result include generic superpositions…

One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…

A system of fluid-dynamic-type equations and their boundary conditions derived from a system of the Boltzmann equation is of great importance in kinetic theory when we are concerned with the motion of a slightly rarefied gas. It offers an…

We review some results concerning the derivation of the Boltzmann equation starting from the many-body classical Hamiltonian dynamics. In particular, the celebrated paper by O. E. Lanford III and the more recent papers [13, 23] are…

We consider a class of phase space measures, which naturally arise in the Bohmian interpretation of quantum mechanics (when written in a Lagrangian form). We study the so-called classical limit of these Bohmian measures, in dependence on…

In this paper we revisit the derivation of boundary conditions for the Boltzmann Equation. The interaction between the wall atoms and the gas molecules within a thin surface layer is described by a kinetic equation introduced in [9] and…