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

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.

Keywords:

• Viscous shallow water system
• Korteweg type
• global well-posedness

AMS Subject Classifications:

• 35Q35
• 35A01

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].