@Article{CMAA-2-2,
author = {Zhigang, Wu and Zhou, Wenyue and Yujie, Li},
title = {Decay of the Compressible Navier-Stokes Equations with Hyperbolic Heat Conduction},
journal = {Communications in Mathematical Analysis and Applications},
year = {2023},
volume = {2},
number = {2},
pages = {115--141},
abstract = {<p style="text-align: justify;">The global solution to the Cauchy problem of the compressible Navier-Stokes equations with hyperbolic heat conduction in dimension three is constructed when the initial data in $H^3$ norm is small. By using several elaborate energy functionals together with the interpolation trick, we simultaneously obtain the optimal $L^2$-decay estimate of the solution and its derivatives when the initial data is bounded in negative Sobolev (Besov) space or $L^1(\mathbb{R}^3).$ Specially speaking, the fluid density, the fluid velocity and the fluid temperature in $L^2$-norm have the same decay rate as the Navier-Stokes-Fourier equations, while the flux $q$ has faster $L^2$-decay rate as $(1+t)^{−2}.$ Our proof is based on a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis for a 8×8 Green matrix of the system. To the best of our knowledge, it is the first result on the large time behavior of this system.</p>},
issn = {2790-1939},
doi = {https://doi.org/10.4208/cmaa.2022-0022},
url = {https://global-sci.com/article/81415/decay-of-the-compressible-navier-stokes-equations-with-hyperbolic-heat-conduction}
}