Related papers: Regularity for the Boltzmann equation conditional …
This is the first one of two papers on the global dynamics of the original Boltzmann equations without angular cutoff on the torus. We address the problem for the hard potentials and Maxwellian molecules in the present paper. The case of…
In this work we consider the classical non-linear Boltzmann equation, where the unknown is the distribution function $f$, which depends on the time $t$, the vector $\mathbf{x}$ (the position of a molecule) and its velocity $\mathbf{\xi}$.…
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…
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…
Departing from the weak solution, we prove the uniqueness, smoothing estimates and the global dynamics for the non cutoff spatially homogeneous Boltzmann equation with moderate soft potentials. Our results show that the behavior of the…
In this paper we study the regularity of the non-cutoff Vlasov-Poisson-Boltzmann system for plasma particles of two species in the whole space $\mathbb{R}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions…
For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space $\mathbb R^3_x$, we establish pointwise lower bounds that appear instantaneously even if the initial data contains vacuum regions. Our lower bounds…
The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyse the…
We construct bounded classical solutions of the Boltzmann equation in the whole space without specifying any limit behaviors at the spatial infinity and without assuming the smallness condition on initial data. More precisely, we show that…
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…
In the present work, we investigate estimates of regularity for weak solutions to the non-cutoff Boltzmann equation with soft potentials. We restrict our focus to the so-called "typically rough and slowly decaying data", which is…
This is a continuation of our series of works for the inhomogeneous Boltzmann equation. We study qualitative properties of classical solutions, precisely, the full regularization in all variables, uniqueness, non-negativity and convergence…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
We consider the non-cutoff Boltzmann equation in the spatially inhomogeneous, soft potentials regime, and establish decay estimates for large velocity. In particular, we prove that pointwise algebraically decaying upper bounds in the…
In the paper we study a measure version of the evolutionary nonlinear Boltzmann-type equation in which we admit a random number of collisions of particles. We consider first a stationary model and use two methods to find its fixed points:…
Collective orders and photo-induced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can…
Difference Boltzmann Equation is derived in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors is used as the second…
We consider the spatially inhomogeneous Boltzmann equation without angular cutoff for soft potentials. For any given initial datum such that the mass, energy and entropy densities are bounded and the mass is away from vacuum, we establish…
We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each…
The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter $c>c_0$ for a properly large and positive $c_0$. A local existence…