Related papers: A second order constitutive theory for polyatomic …
Although the mesoscopic Boltzmann equation describes the rarefied gas dynamics, finding its solutions in complicated engineering problems is challenging. Therefore, over the past one and a half centuries, many partial differential equations…
A complete thermodynamical analysis for a binary mixture of viscous Korteweg fluids with two velocities and two temperatures is developed. The constitutive functions are allowed to depend on the diffusion velocity and the specific internal…
The objective of this work is to determine the nonlinear flux-force relations for systems out of Onsager's region that respect the existing thermodynamic theorems for systems far from equilibrium. To this aim, a thermodynamic theory for…
In the Second Order Theories (SOT) of real relativistic fluids, the non-ideal properties are described by a new set of dynamical tensor variables. In this work we explore the non-linear dynamics of those modes in a conformal fluid. Among…
Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires to derive constitutive relations for…
Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the ``degree of nonequilibrium'', and has a very…
Subject of this paper is the derivation of a new constitutive law in terms of the logarithm of the conformation tensor that can be used as a full substitute for the 2D governing equations of the Oldroyd-B, Giesekus and other models. One of…
Continuum-based theories, such as Navier-Stokes equations, have been considered inappropriate for flows under nonequilibrium conditions. In part, it is due to the lack of rotational degrees of freedom in the Maxwell-Boltzmann distribution.…
A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a…
There are several reasons to extend the presentation of Navier-Stokes equations to multicomponent systems. Many technological applications are based on physical phenomena that are present neither in pure elements nor in binary mixtures.…
Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of \emph{incompressible} fluids is nowadays available not only for Navier--Stokes fluids but also for various…
Two-dimensional turbulence governed by the so-called $\alpha$ turbulence equations, which include the surface quasi-geostrophic equation ($\alpha=1$), the Navier--Stokes system ($\alpha=2$), and the governing equation for a shallow flow on…
We construct an ensemble of two-dimensional nonintegrable quantum circuits that are chaotic but have a conserved particle current, and thus a finite Drude weight. The long-wavelength hydrodynamics of such systems is given by the…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
The steady compressible Navier--Stokes--Fourier system is considered, with either Dirichlet or Navier boundary conditions for the velocity and the heat flux on the boundary proportional to the difference of the temperature inside and…
The linear integral equations defining the Navier-Stokes (NS) transport coefficients for polydisperse granular mixtures of smooth inelastic hard disks or spheres are solved by using the leading terms in a Sonine polynomial expansion.…
The stationary Navier-Stokes equations for a non-Newtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlet type boundary conditions. The viscosity is supposed to depend on the temperature and the…
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…
The Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the…
A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance…