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arXiv · 2209.10773

Asymptotic stability of rarefaction waves for compressible Navier-Stokes equations with relaxation

Yuxi Hu·Xuefang Wang
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Abstract

The asymptotic stability of rarefaction wave for 1-d relaxed compressible isentropic Navier-Stokes equations is established. For initial data with different far-field values, we show that there exists a unique global in time solution. Moreover, as time goes to infinity, the obtained solutions are shown to converge uniformly to rarefaction wave solution of $p$-system with corresponding Riemann initial data. The proof is based on $L^2$ energy methods.

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Yuxi Hu, Xuefang Wang. 2022-09-22. Asymptotic stability of rarefaction waves for compressible Navier-Stokes equations with relaxation. https://arxiv.org/abs/2209.10773

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