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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 16
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Articles

Global well-posedness for the viscous shallow water system with Korteweg type

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Pages 2865-2879 | Received 03 Jun 2017, Accepted 11 Oct 2017, Published online: 31 Oct 2017
 

ABSTRACT

In this paper, we study the Cauchy problem for a viscous shallow water system with Korteweg type in Sobolev spaces. We first establish the local well-posedness of the solution by using the Friedrich method and compactness arguments. Then, we prove the global existence of the solution to the system for the small initial data.

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Acknowledgements

The authors thank the referees for their valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NNSFC [grant number 11671407], [grant number 11271382]; FDCT [grant number 098/2013/A3]; Guangdong Special Support Program [grant number 8-2015]; the key project of NSF of Guangdong province [grant number 2016A030311004].

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