Spectral analysis and hydrodynamic manifolds for the linearized Shakhov model
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.
scientific article; zbMATH DE number 7814528
scientific article