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Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-dependent Viscosity

Year: 2010

Type: preprint

Abstract: In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is constructed by approximating the system and regularizing the initial values which may contain vacuum state. Then some global in time estimates on the weak solution are obtained. Based on these uniform estimates, the vacuum states are shown to vanish in finite time and the weak solution we constructed becomes a unique strong one. Consequently, the stability of the rarefaction wave is proved in a weak sense. The theory holds for large-amplitudes rarefaction waves and arbitrary initial perturbations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1004.0036

Authors: Jiu, Quansen, Wang, Yi, Xin, Zhouping

Institutions: Chinese University of Hong Kong, Capital Normal University, Chinese Academy of Sciences

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Chinese University of Hong Kong

OpenAlex ID: W4310002633

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