关于弱激波的Chapman-Enskog展开有效性的研究

关于精确流体动力学与Chapman-Enskog级数的关系

On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series

本文证明Chapman-Enskog级数在Knudsen数趋于零时局部等价于精确谱闭包，但该级数在非平衡态发散，而精确谱闭包流体动力学对任意Knudsen数全局有效。

Relativistic equations for the generalized Chapman-Enskog hierarchy

From the Boltzmann equation Chapman and Cowling have firstly motivated a hierarchy of differential equations. I consider a general version of these differential equations which contain the Navier-Stokes system. In the paper I derive a relativistic version of these partial differential equations. This is interesting because in the derivation a covariant version of a time direction is used. This time direction is needed to derive a reduction of the differential equations.

剪切分子种子：一种针对一阶 Chapman-Enskog 偏应力的算子级必要性结果

Molecular Seeds of Shear: An operator-level necessity result for first-order Chapman-Enskog deviatoric stress

本文通过证明一阶 Chapman-Enskog 修正非零的必要性，揭示了偏应力在流体极限中的生成条件，并通过 BGK 例子验证了相关算子和传输系数。

Existence of quasilinear relaxation shock profiles

We establish existence with sharp rates of decay and distance from the Chapman--Enskog approximation of small-amplitude quasilinear relaxation shocks in the general case that the profile ODE may become degenerate. Our method of analysis follows the general approach used by Métivier and Zumbrun in the semilinear case, based on Chapman--Enskog expansion and the macro--micro decomposition of Liu and Yu. In the quasilinear case, however, we find it necessary to apply a parameter-dependent Nash-Moser iteration to close the analysis, whereas, in the semilinear case, a simple contraction-mapping argu…

Derivation of the Isotropic Diffusion Source Approximation (IDSA) for Supernova Neutrino Transport by Asymptotic Expansions

We present Chapman--Enskog and Hilbert expansions applied to the $\BigO(v/c)$ Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman--Enskog or Hilbert expansions with reaction and collision scaling. We also give asymptotically sharp results obtained by the use of an additional time scaling. The diffusion limit determines the diffusion source in the \emph{Isotropic …

Center manifolds for a class of degenerate evolution equations and existence of small amplitude kinetic shocks

We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium ow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dyn…