### Electronic Research Archive

2020, Issue 4: 1545-1562. doi: 10.3934/era.2020081
Special Issues

# Global weak solutions for the two-component Novikov equation

• 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142