Related papers: Hilbert's 6th Problem: Exact and Approximate Hydro…
Despite its conceptual and practical importance, the rigorous derivation of the steady incompressible Navier-Stokes-Fourier system from the Boltzmann theory has been {an} outstanding {open problem} for general domains in 3D. We settle this…
The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garz\'o, Brito and Soto, Phys. Fluids \textbf{33}, 023310 (2021)] is considered further to analyze two different problems.…
We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local…
This paper is devoted to the hydrodynamic limit for the linear Boltzmann equation, in the case of a heavy tail equilibrium and a cross section which depends on the space variable and which degenerates for large velocities, without symmetry…
The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as…
Here we derive the relativistic resistive dissipative second-order magnetohydrodynamic evolution equations using the Boltzmann equation, thus extending our work from the previous paper…
Starting with the relativistic Boltzmann equation where the collision term was generalized to include gradients of the phase-space distribution function, we recently presented a new derivation of the equations for the relativistic…
The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied…
We show that macroscopic irreversible thermodynamics for viscous fluids can be derived from exact information-theoretic thermodynamic identities valid at the microscale. Entropy production, in particular, is a measure of the loss of…
We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The problem of reduced description is studied as a problem of constructing the slow…
We study anisotropic fluid dynamics derived from the Boltzmann equation based on a particular choice for the anisotropic distribution function within a boost-invariant expansion of the fluid in one spatial dimension. In order to close the…
The eigenfunctions and eigenvalues of the linearized Boltzmann equation for inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic modes, are calculated in the long wavelength limit for a granular gas. The transport…
We exactly solve the one-dimensional boost-invariant Boltzmann equation in the relaxation time approximation for arbitrary shear viscosity. The results are compared with the predictions of viscous and anisotropic hydrodynamics. Studying…
We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…
We apply the projection operator formalism to the problem of determining the asymptotic behavior of the lattice BGK equation in the hydrodynamic limit. As an alternative to the more usual Chapman-Enskog expansion, this approach offers many…
In the paper the possible approaches to the rigorous derivation of the Boltzmann kinetic equation with hard sphere collisions from underlying dynamics are considered. In particular, a formalism for the description of the evolution of…
We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and…
We derive hydrodynamic equations from Vicsek-style dry active matter models in three dimensions (3D), building on our experience on the 2D case using the Boltzmann-Ginzburg-Landau approach. The hydrodynamic equations are obtained from a…
We derive the general analytical solution of the viscous hydrodynamic equations for an ultrarelativistic gas of hard spheres undergoing Bjorken expansion, taking into account effects from particle number conservation, and use it to…
Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…