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

Citation:

Lining TONG,Yanyan SUN.Local Strong Solutions for the Compressible Non- Newtonian Models with Density-Dependent Viscosity and Vacuum[J].Chinese Annals of Mathematics B,2020,41(3):371~382
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Authors:

Lining TONG; Yanyan SUN

Foundation:

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

Keywords:

Compressible non-Newtonian fluid, Density dependent, Vacuum

Classification:

76N10,\ 35M10,\ 35Q30
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