2010
DOI: 10.4310/maa.2010.v17.n3.a3
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Asymptotic Stability of Viscous Shock Wave for a Onedimensional Isentropic Model of Viscous Gas with Density Dependent Viscosity

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Cited by 34 publications
(30 citation statements)
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“…Under the assumption that the viscous coefficient is given as a power function of density, any viscous shock wave is shown to be nonlinear stable for small initial perturbations with integral zero. In contrast to previous related results [20,22], there is no restrictions on the power index of the viscous coefficient and the amplitudes of the viscous shock wave in our result.…”
contrasting
confidence: 99%
See 1 more Smart Citation
“…Under the assumption that the viscous coefficient is given as a power function of density, any viscous shock wave is shown to be nonlinear stable for small initial perturbations with integral zero. In contrast to previous related results [20,22], there is no restrictions on the power index of the viscous coefficient and the amplitudes of the viscous shock wave in our result.…”
contrasting
confidence: 99%
“…Especially, for isentropic flow, this dependence of the viscosity is translated into the dependence on the density. For more physical background, please refer to [12,22] and references therein.…”
Section: Introductionmentioning
confidence: 99%
“…For the existence of global smooth solutions, the reders are referred to [28], [39] and [41]. Based on the above preparation, we now make some new the uniform estimates with respect to ε for the solutions (ρ ε , u ε ) of the α-CNS (1.1)-(1.2).…”
Section: Uniform Estimates For the Solutions Of α-Cnsmentioning
confidence: 99%
“…In view of the Chapman-Enskog expansion theory for rarefied gas dynamics (cf. [4,7,13]), the viscosity is temperature-dependent, thus density-dependent in the isentropic flow [17], see also [21].…”
Section: Introductionmentioning
confidence: 99%
“…Matsumura-Nishihara [23] and Goodman [6] first studied the stability of viscous shock wave under a zero mass condition. Since then, there have been a large of literatures on this topic and various approaches and techniques like weighted characteristics, approximate Green functions and pointwise estiamtes are developed, see [14,15,16,18,19,12,26,9,24,20,21,27,28] and references therein. It is noted that most of above works require the strength of shock wave is suitably small, that is, the shock is weak.…”
Section: Introductionmentioning
confidence: 99%