相关论文: Measure Valued Solution to the Spatially Homogeneo…

We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We construct a family of special solutions, which are neither near…

In this paper, we study the polyatomic Boltzmann equation based on continuous internal energy, focusing on physically relevant collision kernels of the hard potentials type with integrable angular part. We establish three main results:…

This work is concerned with the generation of decay estimates in the velocity variable for solutions of the space-inhomogeneous Boltzmann equation without cutoff on a bounded spatial domain for hard and moderately soft potentials. We work…

In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation…

We establish pointwise polynomial decay estimates in velocity space for the spatially inhomogeneous Boltzmann equation without cutoff, in the case of hard potentials ($\gamma +2s > 2$), under the assumption that the mass, energy, and…

We consider the spatially inhomogeneous non-cutoff Boltzmann equation with hard potentials in the non-perturbative setting. For initial data with polynomial decay in the velocity variable, we establish the local-in-time existence and…

Maxwell models for nonlinear kinetic equations have many applications in physics, dynamics of granular gases, economy, etc. In the present manuscript we consider such models from a very general point of view, including those with arbitrary…

This article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our…

In this paper we study the Cauchy problem associated to the Maxwell-Schr\"odinger system with a defocusing pure-power non-linearity. This system has many applications in physics, for instance in the description of a charged non-relativistic…

The model of inelastic Maxwell particles (IMP) allows one to derive some exact results which show the strong influence of inelasticity on the nonequilibrium properties of a granular gas. The aim of this work is to propose a simple model…

We prove global existence of smooth solutions near Maxwellians for the non-cutoff Vlasov-Poisson-Boltzmann system in the weakly collisional regime. To address the weak dissipation of the non-cutoff linearized Boltzmann operator, we develop…

For a massless gas with constant cross section in a homogeneous, isotropically expanding spacetime we reformulate the relativistic Boltzmann equation as a set of non-linear coupled moment equations. For a particular initial condition this…

The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…

A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…

We present a spectral Petrov-Galerkin method for the Boltzmann collision operator. We expand the density distribution $f$ to high order orthogonal polynomials multiplied by a Maxwellian. By that choice, we can approximate on the whole…

This paper deals with the long time behavior of solutions to the spatially homogeneous Boltzmann equation. The interactions considered are the so-called (non cut-off and non mollified) hard potentials. We prove an exponential in time…

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,…

We prove an inequality on the Kantorovich-Rubinstein distance --which can be seen as a particular case of a Wasserstein metric-- between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, but with a…

In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from the initial data and collision kernel is studied. Well-posedness and long-time behavior - exponential decay to the global equilibrium - of the…

In order to solve the Boltzmann equation numerically, in the present work, we propose a new model equation to approximate the Boltzmann equation without angular cutoff. Here the approximate equation incorporates Boltzmann collision operator…