Boltzmann and Vlasov equations played a great role in the past and still play an important
role in modern natural sciences, technique and even philosophy of science. Classical …

The aim of this book is to present some mathematical results describing the transition from
kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to …

We prove that the renormalized solutions of the Boltzmann equation considered in a
bounded domain with different types of (kinetic) boundary conditions converge to the Stokes …

The present book aims at presenting in a systematic, painstaking and rather exhaustive
manner the incompressible viscous fluid limits of the system of Vlasov–Maxwell–Boltzmann …

Abstract Systems coupling fluids and polymers are of great interest in many branches of
sciences. One of the most classical models to describe them is the FENE (Finite Extensible …

The classical models of fluid dynamics, such as the Euler or Navier–Stokes equations, were
first established by applying Newton's second law of motion to each infinitesimal volume …

We establish the incompressible Navier‐Stokes‐Fourier limit for solutions to the Boltzmann
equation with a general cutoff collision kernel in a bounded domain. Appropriately scaled …

We establish the convergence to the equilibrium for various linear collisional kinetic
equations (including linearized Boltzmann and Landau equations) with physical local …

In a general C 1 domain, we study the perturbative Cauchy theory for the Boltzmann
equation with Maxwell boundary conditions with an accommodation coefficient α in (2/3, 1] …

The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied
gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated …