Multiscale Hilbert expansion and hydrodynamics beyond Navier-Stokes

2025/08/26 by O. M. Chekmareva, Chekmareva, O. M., I. B. Chekmarev +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2509.02580

openalex publication_date 2025/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A truncated Hilbert expansion with multiple scales is used to construct asymptotic solution of the linearized one-dimensional Boltzmann equation with small Knudsen number. The freedom ganed by introducing new independent time variables is exploited to eliminate the sources of secular behavior as the time interval increases. The regular gas-dynamic equations then appear as necessary conditions for expansion to be uniformly valid on a long time intervals.

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