Global weak solutions for the two-component Novikov equation

Cheng He; Changzheng Qu; Cheng He; Changzheng Qu

doi:10.3934/era.2020081

Electronic Research Archive

2020, Volume 28, Issue 4: 1545-1562. doi: 10.3934/era.2020081

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Global weak solutions for the two-component Novikov equation

Cheng He ,
Changzheng Qu

School of Mathematics and Statistics and Center for Nonlinear Studies, Ningbo University, Ningbo 315211, China

Received: 01 May 2020 Revised: 01 July 2020 Published: 31 July 2020
37K05, 37K10

The two-component Novikov equation is an integrable generalization of the Novikov equation, which has the peaked solitons in the sense of distribution as the Novikov and Camassa-Holm equations. In this paper, we prove the existence of the $ H^1 $-weak solution for the two-component Novikov equation by the regular approximation method due to the existence of three conserved densities. The key elements in our approach are some a priori estimates on the approximation solutions.
- Novikov equation,
- two-component Novikov equation,
- Camassa-Holm equation,
- weak solution,
- peaked solution,
- conservation law
Citation: Cheng He, Changzheng Qu. Global weak solutions for the two-component Novikov equation[J]. Electronic Research Archive, 2020, 28(4): 1545-1562. doi: 10.3934/era.2020081

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Abstract

The two-component Novikov equation is an integrable generalization of the Novikov equation, which has the peaked solitons in the sense of distribution as the Novikov and Camassa-Holm equations. In this paper, we prove the existence of the $ H^1 $-weak solution for the two-component Novikov equation by the regular approximation method due to the existence of three conserved densities. The key elements in our approach are some a priori estimates on the approximation solutions.

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