Spectral analysis and hydrodynamic manifolds for the linearized Shakhov model
type: Item
instance of: scholarly article
title: Spectral analysis and hydrodynamic manifolds for the linearized Shakhov model
arXiv ID: 2305.06612
author: Florian Kogelbauer
author: I. V. Karlin
published in: Physica D
publication date: 2024-03-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/2305.06612
review text: The authors performed a complete spectral analysis of the linearized Shakhov model involving two relaxation times \(\tau_{\mathrm{fast}}\) and \(\tau_{\mathrm{slow}}\). Their results are based on spectral functions derived from the theory of finite-rank perturbations, thus they can derive an explicit expression for the critical wave number \(k_{\mathrm{crit}}\) limiting the number of discrete eigenvalues above the essential spectrum together with the existence of a finite-dimensional slow manifold defining non-local hydrodynamics. Further, they discussed the merging of hydrodynamic modes as well as the existence of second sound and the appearance of ghost modes beneath the essential spectrum in dependence on the Prandtl number. Their proof is based on the theory of finite-rank perturbations, together with some properties of the plasma dispersion function, collected in the Appendix for the sake of completeness. Furthermore, the authors give a hydrodynamic interpretation of the results by considering the dynamics of the slow hydrodynamic manifold (linear combination of eigenspaces) up to the explicit calculation of generalized transport coefficients.
reviewed by: Lingda Xu
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 35Q20
zbMATH DE Number: 7814528
zbMATH Keywords: kinetic theory
zbMATH Keywords: second sound existence
zbMATH Keywords: hydrodynamic closure
zbMATH Keywords: finite-rank perturbation
zbMATH Keywords: critical wave number
MaRDI profile type: Publication
OpenAlex ID: W4389305831
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DOI: 10.1016/J.PHYSD.2023.134014
description: scientific article; zbMATH DE number 7814528