相关论文: Quantitative relaxation towards equilibrium for so…

The Cauchy problem for the Boltzmann equation with soft potential, in the framework of small perturbation of an equilibrium state, has been studied in many spaces. The method of strongly continuous semigroup has been applied by…

We establish the $L^1$ weighted propagation properties for solutions of the Boltzmann equation with hard potentials and non-integrable angular components in the collision kernel. Our method identifies null forms by angular averaging and…

REVISED VERSION INCORPORATING THE ERRATUM ON LEMMA 2.1 AND WITH A CORRECTION TO LEMMA 2.8 In this paper we derive optimal relaxation rates for the Cahn-Hilliard equation on the one-dimensional torus and the line. We consider initial…

In this article, we study the continuous mild solutions to the Boltzmann equation in a bounded spatial domain, under either angular cutoff assumption or non-cutoff assumption. Without assuming convexity of the spatial domain, we establish a…

We construct a unique global solution to the Cauchy problem of the 3D Boltzmann equation for initial data around the Maxwellian in the spatially critical homogeneous Besov space…

For a homogenization problem associated to a linear elliptic operator, we prove the existence of a distributional corrector and we find an approximation scheme for the homogenized coefficients. We also study the convergence rates in the…

In this paper, we consider a particular class of solutions to the Boltzmann equation which are referred to as homoenergetic solutions. They describe the dynamics of a dilute gas due to collisions and the action of either a shear, a dilation…

We prove rate of convergence results for singular perturbations of Hamilton-Jacobi equations in unbounded spaces where the fast operator is linear, uniformly elliptic and has an Ornstein-Uhlenbeck-type drift. The slow operator is a fully…

We study Boltzmann-Fermi-Dirac equation when quantum effects are taken into account in dilute gas dynamics. By employing new estimates on trilinear terms of collision kernels, we prove the global existence of the classical solution to…

We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-$\frac{1}{2}$ particles, starting from a general quantum field Hamiltonian. Each…

A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space…

We give a short and elementary proof of stability for strong solutions of the spatially homogeneous Landau equation with Coulomb collisions, measured in relative entropy. The argument yields an explicit differential inequality for relative…

We consider the 2-dimensional spatially homogeneous Boltzmann equation for hard potentials. We assume that the initial condition is a probability measure that has some exponential moments and is not a Dirac mass. We prove some…

The goal of this paper is to give a short review of recent results of the authors concerning classical Hamiltonian many particle systems. We hope that these results support the new possible formulation of Boltzmann's ergodicity hypothesis…

A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…

In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by showing a spectral gap in weighted $L^2$ spaces of the…

One of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonlocal functions of the former. In this paper, we address this…

The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space-time is mapped into a Sturm-Liouville. This mapping gives rise to an effective…

This work is devoted to the study of a relaxation limit of the so-called aggregation equation with a pointy potential in one dimensional space. The aggregation equation is by now widely used to model the dynamics of a density of individuals…

Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many non-interacting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the…