On the Cauchy problem for the new integrable two-component Novikov equation

  • Yongsheng MiEmail author
  • Chunlai Mu


This paper is devoted to a new integrable two-component Novikov equation, lax pairs and bi-Hamiltonian structures. Firstly, the local well-posedness in nonhomogeneous Besov spaces is established by using the Littlewood–Paley theory and transport equations theory. Then, we verify the blow-up that occurs for this system only in the form of breaking waves. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. Finally, we prove that the strong solutions of the system maintain corresponding properties at infinity within its lifespan provided the initial data decay exponentially and algebraically, respectively.


Besov spaces Camassa–Holm-type equation Local well-posedness Persistence properties 

Mathematics Subject Classification

35B30 35G25 35A10 35Q53 



The authors would like to thank the referees for constructive suggestions and comments. The work of Mi is partially supported by NSF of China (11671055), partially supported by NSF of Chongqing (cstc2018jcyjAX0273), partially supported by Key project of science and technology research program of Chongqing Education Commission (KJZD-K20180140).


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsYangtze Normal UniversityChongqingPeople’s Republic of China
  2. 2.College of Mathematics and StatisticsChongqing UniversityChongqingPeople’s Republic of China

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