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Acta Applicandae Mathematicae

, Volume 160, Issue 1, pp 101–128

# Global Well-Posedness of an Initial-Boundary Value Problem of the 2-D Incompressible Navier-Stokes-Darcy System

• Pan Liu
• Wenjuan Liu
Article
• 135 Downloads

## Abstract

We investigate in the paper the initial boundary value problem of the two dimensional incompressible Navier-Stokes-Darcy system in a strip domain. It is shown that, without any small initial data assumption, the Navier-Stokes-Darcy equations have a unique global strong solution in the strip domain with a flat interface. The key is to establish the global-in-time regularity uniformly by pursuing the properties of Dirichlet-Neumann operator.

## Keywords

Navier-Stokes-Darcy system Global well-posedness Dirichlet-Neumann operator

## Mathematics Subject Classification

35A07 74F10 76D03

## Notes

### Acknowledgements

The authors would like to thank Professor Guilong Gui for helpful discussions. This work of the authors is partially supported by the National Natural Science Foundation of China under the grants 11571279 and 11331005. The authors would like to thank the referees for constructive suggestions and comments.

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## Copyright information

© Springer Nature B.V. 2018

## Authors and Affiliations

1. 1.School of MathematicsNorthwest UniversityXi’anChina