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ABSTRACT
Considered herein is the Cauchy problem for a two-component Novikov system. With the application of the method of approximate solutions, we first prove that the solution map of this problem is not uniformly continuous in . Then, we investigate the persistence properties, which implies that the strong solutions of this problem will decay at infinity in the spatial variable provided that the initial data does.
Acknowledgements
The author is grateful to the referees for their helpful comments. The author also thanks the University of Surrey and Dr Bin Cheng in Department of Mathematics for the hospitality received during his visit from March 2016.
Notes
No potential conflict of interest was reported by the author.
Additional information
Funding
This work is partially supported by the Natural Science Foundation of Jiangsu Province [grant number BK20150400]; the Jiangsu Government Scholarship for Overseas Studies and NSFC [grant number 11501309].