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Nonlinear stability of rarefaction waves for a viscous radiative and reactive gas with large initial perturbation
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of an one-dimensional compressible Navier-Stokes type system for a viscous, compressible, radiative and reactive gas, where the constitutive relations for the pressure $p$, the specific internal energy $e$, the specific volume $v$, the absolute temperature $\theta$, and the specific entropy $s$ are given by $p=R\theta/v +a\theta^4/3$, $e=C_v\theta+av\theta^4$, and $s=C_v\ln \theta+ 4av\theta^3/3+R\ln v$ with $R>0$, $C_{v}>0$, and $a>0$ being the perfect gas constant, the specific heat and the radiation constant, respectively. For such a specific gas motion, a somewhat surprising fact is that, general speaking, the pressure $\widetilde{p}(v,s)$ is not a convex function of the specific volume $v$ and the specific entropy $s$. Even so, we show in this paper that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant $a$ and the strength of the rarefaction waves are sufficiently small. The key point in our analysis is to deduce the positive lower and upper bounds on the specific volume and the absolute temperature, which are uniform with respect to the space and the time variables, but are independent of the radiation constant $a$.<br />Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematics
- Subjects :
- Stefan–Boltzmann constant
Internal energy
General Mathematics
010102 general mathematics
Mathematical analysis
Perfect gas
01 natural sciences
010101 applied mathematics
symbols.namesake
Mathematics - Analysis of PDEs
Compressibility
Radiative transfer
symbols
FOS: Mathematics
Initial value problem
0101 mathematics
Entropy (arrow of time)
Absolute zero
Mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....b4bf86d7d15fc2f636adf8cb869fe87b
- Full Text :
- https://doi.org/10.48550/arxiv.2005.00276