The Chapman-Enskog Expansion and the Quantum Hydrodynamic Model for Semiconductor Devices

The Quantum Hydrodynamic Model for Semiconductor Devices

The Regularized Chapman-Enskog Expansion for Scalar Conservation Laws

ROSENAO [R] has recently proposed a regularized version of the ChapmanEnskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at low wave numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. In this paper we study the behavior of the Rosenau regularization o...

Does the Chapman–Enskog expansion for viscous granular flows converge?

This paper deals with the convergence/divergence issue of the Chapman–Enskog series expansion of the shear and normal stresses for a granular gas of inelastic hard spheres. From the exact solution of a simple kinetic model in the uniform shear and longitudinal flows, it is shown that (except in the elastic limit) both series converge and their respective radii of convergence increase with inela...

Regularized Chapman-enskog Expansion for Scalar Conservation Laws

Rosenau Phys. Rev. A, 40 (1989), pp. 7193-6] has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. In this paper we study the behavi...

A Mathematical Pde Perspective on the Chapman–enskog Expansion

This paper presents in a synthetic way some recent advances on hydrodynamic limits of the Boltzmann equation. It aims at bringing a new light to these results by placing them in the more general framework of asymptotic expansions of Chapman–Enskog type, and by discussing especially the issues of regularity and truncation. The present article is one of two companion papers on the Chapman–Enskog ...