Related papers: Moments creation for the inelastic Boltzmann equat…
The initial-boundary value problem for the inhomogeneous non-cutoff Boltzmann equation is a challenging open problem. In this paper, we study the stability and long-time dynamics of the Boltzmann equation near a global Maxwellian without…
In this paper, we consider the spatially inhomogeneous diffusively driven inelastic Boltzmann equation in different cases: the restitution coefficient can be constant or can depend on the impact velocity (which is a more physically relevant…
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…
We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional…
In this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous Boltzmann equation for Bose-Einstein particles for the hard sphere model for bounded anisotropic initial data. The main idea of our…
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…
We consider solutions $f=f(t,x,v)$ to the full (spatially inhomogeneous) Boltzmann equation with periodic spatial conditions $x \in \mathbb T^d$, for hard and moderately soft potentials \emph{without the angular cutoff assumption}, and…
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…
In this paper, we obtain the weak Harnack inequality and H\"older estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cut-off can be written in this form and satisfies our…
In this paper, we study the global existence and uniqueness, Gaussian lower bound, and moment estimates in the spatially homogeneous Boltzmann equation for Fermi-Dirac particles for hard potential ($0\leq \gamma\leq 2$) with angular cutoff…
We prove the well-posedness for the non-cutoff Boltzmann equation with soft potentials when the initial datum is close to the {\it global Maxwellian} and has only polynomial decay at the large velocities in $L^2$ space. As a result, we get…
In this paper, we investigate the problems of Cauchy theory and exponential stability for the inhomogeneous Boltzmann equation without angular cut-off. We only deal with the physical case of hard potentials type interactions (with a…
We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been…
We review and develop the classical theory of moments of configurations of weighted points with a focus on systems with an identically vanishing first moment. The latter condition produces equations for equilibrium configurations of systems…
In this paper, we will introduce a precise classification of characteristic functions in the Fourier space according to the moment constraint in the physical space of any order. Based on this, we construct measure valued solutions to the…
We consider a modified Boltzmann equation which contains, together with the collision operator, an additional drift term that is characterized by a matrix A. Furthermore, we consider a Maxwell gas, where the collision kernel has an angular…
Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner…
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…
The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials $(-4\le \gm<0$), with and without angular cutoff. We prove the time-averaged $L^1$-convergence to…