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Local Strong Solutions for the Compressible Non-Newtonian Models with Density-Dependent Viscosity and Vacuum

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Abstract

The one-dimensional compressible non-Newtonian models are considered in this paper. The extra-stress tensor in our models satisfies a kind of power law structure which was proposed by O. A. Ladyzhenskaya in 1970s. In particular, the viscosity coefficient in our models depends on the density. By using energy-estimate, the authors obtain the existence and uniqueness of local strong solutions for which the density is non-negative.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Lining Tong & Yanyan Sun

Authors
  1. Lining Tong
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  2. Yanyan Sun
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Correspondence to Lining Tong or Yanyan Sun.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11371240, 11771274, 11901379).

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Tong, L., Sun, Y. Local Strong Solutions for the Compressible Non-Newtonian Models with Density-Dependent Viscosity and Vacuum. Chin. Ann. Math. Ser. B 41, 371–382 (2020). https://doi.org/10.1007/s11401-020-0204-y

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  • DOI: https://doi.org/10.1007/s11401-020-0204-y

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