Persistence properties for the two-component Novikov equation in weighted L^p spaces

ABSTRACT

This paper deals with the Cauchy problem of two-component Novikov equation, and the system was proposed by Popowicz. We mainly investigate the persistence properties of strong solutions in weighted $L_{\varphi }^p:=L^p(\mathbb{R},{\varphi }^p(x)\mathrm{d}x)$ spaces for a large class of moderate weights. Our results extends the work of Brandolese on persistence properties of the Camassa-Holm equation to more general system with cubic nonlinearity and interaction between the two components.

KEYWORDS:

• Two-component Novikov equation
• persistence properties
• weighted $L^p$ spaces

AMS SUBJECT CLASSIFICATIONS:

• 35G25
• 35L05
• 35Q50

Acknowledgements

The authors are very grateful to the anonymous reviewers and editors for their careful reading and useful suggestions, which greatly improved the presentation of the paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partly supported by the Science and Technology Research Program of Chongqing Municipal Education Commission [grant number KJ1703043]; Natural Science Foundation of Chongqing [grant number cstc2017jcyjAX0123].