Related papers: On uniqueness and stability for the Enskog equatio…
In this work we prove an analogue, for partial differential equations on the space of probability measures, of the classical vanishing viscosity result known for equations on the Euclidean space. Our result allows in particular to show that…
This paper investigates the dynamic properties of a confined quasi-two-dimensional granular fluid at moderate densities, modeled within the framework of the Enskog kinetic equation. The system is described using the so-called…
We consider a perturbation of a Hilbert space-valued Ornstein--Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls…
As extensions to the corresponding results derived for time homogeneous McKean- Vlasov SDEs, the exponential ergodicity is proved for time-periodic distribution dependent SDEs in three different situations: 1) in the quadratic Wasserstein…
The Navier-Stokes transport coefficients for a model of a confined quasi-two-dimensional granular gas of smooth inelastic hard spheres are derived from the Enskog kinetic equation. A normal solution to this kinetic equation is obtained via…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account…
The space-time development of a quark-gluon plasma is calculated from a Vlasov equation for the distribution function of quasiparticles with medium dependent masses. At each space-time point the masses are calculated selfconsistently from a…
The time evolution of a homogeneous bidisperse granular suspension is studied in the context of the Enskog kinetic equation. The influence of the surrounding viscous gas on the solid particles is modeled via a deterministic viscous drag…
We present a simple approach to study the one-dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of…
We consider the sedimentation of $N$ spherical particles with identical radii $R$ in a Stokes flow in $\mathbb R^3$. The particles satisfy a no-slip boundary condition and are subject to constant gravity. The dynamics of the particles is…
Based on the weak existence and weak uniqueness, we study the pathwise uniqueness of the solutions for a class of one-dimensional stochastic differential equations driven by pure jump processes. By using Tanaka's formula and the local time…
The hydrodynamic equation governing the homogeneous time evolution of the temperature in a model of confined granular gas is studied by means of the Enskog equation. The existence of a normal solution of the kinetic equation is assumed as a…
Caustics-envelopes formed by the trajectories of fluid particles-arise in proposed dynamical extensions for shell-crossing singularities occurring in the Einstein-dust system. In this study, a local existence result is established,…
In this paper, we sketch the proof of the extension of the stability theorem of the Minkowski space in General Relativity done explicitly in previous work by the present author. We discuss solutions of the Einstein vacuum (EV) equations. We…
We consider Mc Kean-Vlasov stochastic differential equations (MVSDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. This type of SDEs…
We study a class of non linear integro-differential equations on the Wasserstein space related to the optimal control of McKean--Vlasov jump-diffusions. We develop an intrinsic notion of viscosity solutions that does not rely on the lifting…
The transport coefficients of a granular fluid driven by a stochastic bath with friction are obtained by solving the inelastic Enskog kinetic equation from the Chapman-Enskog method. The heat and momentum fluxes as well as the cooling rate…
Minkowski space is shown to be globally stable as a solution to the massive Einstein--Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying…
The goal of this note is to provide most of the technical details involved in the application of the Chapman-Enskog method to solve the revised Enskog equation to Navier-Stokes order. Explicit expressions for the transport coefficients and…