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One-dimensional Compressible Navier--Stokes Equations with Temperature Dependent Transport Coefficients and Large Data

Hongxia Liu Tong Yang Huijiang Zhao Qingyang Zou

Analysis of PDEs mathscidoc:1912.43947

SIAM Journal on Mathematical Analysis, 46, (3), 2185-2228, 2014.6
This paper is concerned with the Cauchy problem of the one-dimensional compressible Navier--Stokes equations with degenerate temperature dependent transport coefficients which satisfy conditions from the consideration in kinetic theory. A result on the existence and uniqueness of a globally smooth nonvacuum solution is obtained provided that the -norm of the initial perturbation) for some positive constant independent of . Here is the adiabatic gas constant. This is a Nishida--Smoller type global solvability result with large data.
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@inproceedings{hongxia2014one-dimensional,
  title={One-dimensional Compressible Navier--Stokes Equations with Temperature Dependent Transport Coefficients and Large Data},
  author={Hongxia Liu, Tong Yang, Huijiang Zhao, and Qingyang Zou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210831708300511},
  booktitle={SIAM Journal on Mathematical Analysis},
  volume={46},
  number={3},
  pages={2185-2228},
  year={2014},
}
Hongxia Liu, Tong Yang, Huijiang Zhao, and Qingyang Zou. One-dimensional Compressible Navier--Stokes Equations with Temperature Dependent Transport Coefficients and Large Data. 2014. Vol. 46. In SIAM Journal on Mathematical Analysis. pp.2185-2228. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210831708300511.
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