Contact discontinuity with general perturbations for gas motions

Feimin Huang Zhouping Xin Tong Yang

Analysis of PDEs mathscidoc:1912.43929

Advances in Mathematics, 219, (4), 1246-1297, 2008.11
The contact discontinuity is one of the basic wave patterns in gas motions. The stability of contact discontinuities with general perturbations for the NavierStokes equations and the Boltzmann equation is a long standing open problem. General perturbations of a contact discontinuity may generate diffusion waves which evolve and interact with the contact wave to cause analytic difficulties. In this paper, we succeed in obtaining the large time asymptotic stability of a contact wave pattern with a convergence rate for the NavierStokes equations and the Boltzmann equation in a uniform way. One of the key observations is that even though the energy norm of the deviation of the solution from the contact wave may grow at the rate (1+ t) 1 4, it can be compensated by the decay in the energy norm of the derivatives of the deviation which is of the order of (1+ t) 1 4. Thus, this reciprocal order of decay rates for the time
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@inproceedings{feimin2008contact,
  title={Contact discontinuity with general perturbations for gas motions},
  author={Feimin Huang, Zhouping Xin, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210724429261493},
  booktitle={Advances in Mathematics},
  volume={219},
  number={4},
  pages={1246-1297},
  year={2008},
}
Feimin Huang, Zhouping Xin, and Tong Yang. Contact discontinuity with general perturbations for gas motions. 2008. Vol. 219. In Advances in Mathematics. pp.1246-1297. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210724429261493.
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