Kinetic approach to generalized hydrodynamics

Abstract

The hydrodynamic behavior of fluids in the finite-(k,ω) region is usually described by means of generalized hydrodynamics through (k,ω)-dependent transport coefficients. Here we have developed Grad’s-solution method for solving the Boltzmann equation up to 26 moments; the fluxes associated with the heat flow and the viscosity tensor are considered physically relevant for the description of the system. We obtain the characteristic equations of the generalized hydrodynamics scheme and the following additional results: (i) some particular stationary solutions leading to the usual transport coefficients; (ii) constitutive equations for the viscous tensor and the heat flux, which in the wave-vector space lead to k-dependent transport coefficients; (iii) Maxwell-Cattaneo-like equations in nonstationary states with relaxation times expressed in terms of collision integrals; and (iv) the (k,ω)-dependent transport coefficients associated with the generalized hydrodynamic regime and their relationship with the relaxation times associated with the fluxes.