Abstract
<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">$ H^1 $</tex-math></inline-formula>-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.</p>
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