## Abstract

We consider the Cauchy problem for one-dimensional (1D) barotropic compressible Navier-Stokes equations with density-depending viscosity and large external forces. Under a general assumption on the density-depending viscosity, we prove that the Cauchy problem admits a unique global strong (classical) solution for the large initial data with vacuum. Moreover, the density is proved to be bounded from above time-independently. As a consequence, we obtain the large time behavior of the solution without external forces.

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## Acknowledgements

This work was supported by Undergraduate Research Fund of Beijing Normal University (Grant Nos. 2017-150 and 201810027047), and National Natural Science Foundation of China (Grant Nos. 11601218 and 11771382).

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Li, K., Lü, B. & Wang, Y. Global well-posedness and large-time behavior of 1D compressible Navier-Stokes equations with density-depending viscosity and vacuum in unbounded domains.
*Sci. China Math.* **64**, 1231–1244 (2021). https://doi.org/10.1007/s11425-019-9521-4

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DOI: https://doi.org/10.1007/s11425-019-9521-4

### Keywords

- 1D compressible Navier-Stokes equations
- global well-posedness
- large initial data
- vacuum
- density-depending viscosity