Related papers: Existence and uniqueness of $L^p$ solutions to the…

This paper reviews results on the scalar Boltzmann equation for a single-component polyatomic gas with continuous internal energy. For the space homogeneous problem, $L^1$-theory is established, for solutions with initial strictly positive…

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel…

We prove the Hardy-Littlewood-Sobolev type $L^p$ estimates for the gain term of the Boltzmann collision operator including Maxwellian molecule, hard potential and hard sphere models. Combining with the results of Alonso et al. [2] for the…

We derive the 3D spatially homogeneous Boltzmann's equation with moderately soft potentials and singular angular interaction, from an interacting particles system. The collision kernel is of the form $B(z,\sigma)=|z|^{\gamma}b\left(…

We establish a priori estimates showing the propagation and generation of $L^p$-norms for solutions to the non-cutoff spatially homogeneous Boltzmann equation with soft potentials. The singularity of the collision kernel is key to generate…

The Landau equation and the Boltzmann equation are connected through the limit of grazing collisions. This has been proved rigorously for certain families of Boltzmann operators concentrating on grazing collisions. In this contribution, we…

In this paper we prove the strong and time-averaged strong convergence to equilibrium for solutions (with general initial data) of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. The assumption on the collision…

We prove explicit coercivity estimates for the linearized Boltzmann and Landau operators, for a general class of interactions including any inverse-power law interactions, and hard spheres. The functional spaces of these coercivity…

In this work, we are concerned with the regularities of the solutions to Boltzmann equation with the physical collision kernels for the full range of intermolecular repulsive potentials, $r^{-(p-1)}$ with $p>2$. We give the new and…

This paper proves the existence of weak solutions to the spatially homogeneous Boltzmann equation for Maxwellian molecules, when the initial data are chosen from the space of all Borel probability measures on R^3 with finite second moments…

In this note we study Boltzmann's collision kernel for inverse power law interactions $U_s(r)=1/r^{s-1}$ for $s>2$ in dimension $ d=3 $. We prove the limit of the non-cutoff kernel to the hard-sphere kernel and give precise asymptotic…

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…

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…

In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. The collision kernel considered here is…

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…

In this paper we study the Cauchy problem for the spatially homogeneous relativistic Landau equation with Coulomb interactions. Despite it's physical importance, this equation has not received a lot of mathematical attention we think due to…

We study weak solutions of the homogeneous Boltzmann equation for Maxwellian molecules with a logarithmic singularity of the collision kernel for grazing collisions. Even though in this situation the Boltzmann operator enjoys only a very…

We define and study homogeneous kinetic Sobolev spaces adapted to the Kolmogorov equation. We consider both local and non-local diffusion. The spaces are built from the Lebesgue spaces L p for all integrability exponents p $\in$ (1,…

This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…

We study the Cauchy theory for a multi-species mixture, where the different species can have different masses, in a perturbative setting on the $3$-dimensional torus. The ultimate aim of this work is to obtain existence, uniqueness and…