Related papers: Fourier's Law for a Granular Fluid
We present a selective overview of the current state of our knowledge (more precisely of ourignorance) regarding the derivation of Fourier's Law, ${\bf J}(\br) =-\kappa {\bf \nabla}T(\br)$; ${\bf J}$ the heat flux, $T$ the temperature and…
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…
This paper investigates the asymptotic stability of rarefaction waves for a one-dimensional compressible fluid system, where the Newton's law of viscosity and Fourier's law of heat conduction are replaced by Maxwell's law and Cattaneo's…
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary…
In the classical framework, the Navier-Stokes-Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional…
The system of Navier--Stokes--Fourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the limit when gradients of density, velocity and temperature are sufficiently small,…
The Navier-Stokes granular hydrodynamics is employed for determining the threshold of thermal convection in an infinite horizontal layer of granular gas. The dependence of the convection threshold, in terms of the inelasticity of particle…
A new formulation of the Navier-Stokes equation, in terms of the gradient of the total mechanical energy, is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found.…
The viscous interaction of fluid is understood as the response to deformation, which is proportional to the strain rate. This model has gradually become the standard since Stokes, and has become the basis of the classical flow theory,…
We show that a Galilean invariant version of fluid dynamics can be derived by the methods of statistical dynamics using Maxwell's balance equations. The basic equation is non-local, and might replace Boltzmann's equation if the latter turns…
The existence of two stationary solutions of the nonlinear Boltzmann equation for inelastic hard spheres or disks is investigated. They are restricted neither to weak dissipation nor to small gradients. The one-particle distribution…
We consider the barotropic Navier--Stokes system describing the motion of a compressible Newtonian fluid in a bounded domain with in and out flux boundary conditions. We show that if the boundary velocity coincides with that of a rigid…
The steady motion of a viscous incompressible fluid in a multiply-connected, planar, bounded domain (perforated with a large number of small holes) is modeled through the Navier-Stokes equations with non-homogeneous Dirichlet boundary data…
The light-scattering spectrum for a Maxwell fluid in a steady state due to the presence of an external temperature gradient is computed. In such a fluid heat conduction is assumed to be governed by the classical Fourier law. The calculation…
A kinetic and hydrodynamic descriptions are developed in order to analyze the instabilities of a granular gas in the presence of a gravitational field. In the kinetic description the Boltzmann equation is coupled with the Poisson equation,…
In the continuum flow regime, the Navier-Stokes equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied gas dynamics. Both equations are constructed from modeling…
The similarity between electromagnetics and hydrodynamics has been noticed for a long time. Maxwell developed an analogy, where the magnetic field and the vector potential in electromagnetics are compared to the vorticity and velocity in…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
The Navier-Stokes-Fourier system is a well established model for describing the motion of viscous compressible heat-conducting fluids. We study the existence of time-periodic weak solutions and improve the known result in the following…
In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent "fluid particles" with viscous stress proportional to rate of strain. The crucial…