Compressible Viscous Flows in a Symmetric Domain with Complete Slip Boundary

Kefeng Liu

Analysis of PDEs mathscidoc:1912.43127

arXiv preprint arXiv:1612.07934, 2016.12
This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity lacks decaying structure. In fact, we show the existence of uniformly rotating solutions as steady states for the compressible Navier-Stokes equations. By manipulating the conservation law of angular momentum, we establish a suitable Korn's type inequality to control the perturbation and show the asymptotic stability of the uniformly rotating solutions with small angular velocity. In particular, the initial perturbation which preserves the angular momentum would decay exponentially in time and the solution to the Navier-Stokes equations converges to the steady state as time grows up.
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@inproceedings{kefeng2016compressible,
  title={Compressible Viscous Flows in a Symmetric Domain with Complete Slip Boundary},
  author={Kefeng Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111710179906687},
  booktitle={arXiv preprint arXiv:1612.07934},
  year={2016},
}
Kefeng Liu. Compressible Viscous Flows in a Symmetric Domain with Complete Slip Boundary. 2016. In arXiv preprint arXiv:1612.07934. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111710179906687.
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