Hyperbolicity of exact hydrodynamics for three-dimensional linearized Grad's equations

TL;DR

This paper proves the hyperbolicity of exact three-dimensional linear hydrodynamic equations derived from Grad's moment system and establishes an H-theorem, advancing the theoretical understanding of these models.

Contribution

It extends previous hyperbolicity proofs to three dimensions and provides an H-theorem for the system, enhancing the theoretical foundation of Grad's equations.

Findings

Proof of hyperbolicity for 3D Grad's system

Establishment of an H-theorem for the model

Extension of previous 2D results to 3D

Abstract

We extend a recent proof of hyperbolicity of the exact (to all orders in Knudsen number) linear hydrodynamic equations [M. Colangeli et al, Phys. Rev. E (2007), in press; arXiv:cond-mat/0703791v2] to the three-dimensional Grad's moment system. A proof of an H-theorem is also presented.