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Large-time behavior of solutions to the inflow problem of full compressible NavierStokes equations

Xiaohong Qin Yi Wang

Analysis of PDEs mathscidoc:1912.43757

SIAM Journal on Mathematical Analysis, 43, (1), 341-366, 2011.1
Large-time behavior of solutions to the inflow problem of full compressible NavierStokes equations is investigated on the half line \mathbf{R}_+=(0,+\infty). The wave structure, which contains four wavesthe transonic (or degenerate) boundary layer solution, the 1-rarefaction wave, the viscous 2-contact wave, and the 3-rarefaction wave to the inflow problemis described, and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible NavierStokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the treatments of the degeneracies in the transonic boundary layer solution and the wave interactions in the superposition wave.
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@inproceedings{xiaohong2011large-time,
  title={Large-time behavior of solutions to the inflow problem of full compressible NavierStokes equations},
  author={Xiaohong Qin, and Yi Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205544586700321},
  booktitle={SIAM Journal on Mathematical Analysis},
  volume={43},
  number={1},
  pages={341-366},
  year={2011},
}
Xiaohong Qin, and Yi Wang. Large-time behavior of solutions to the inflow problem of full compressible NavierStokes equations. 2011. Vol. 43. In SIAM Journal on Mathematical Analysis. pp.341-366. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205544586700321.
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