The existence of global weak solutions to the Cauchy problem for the Novikov equation is established in the space C([0, ∞)×R)∩L∞([0, ∞);H1(R)) without the sign condition on the initial value. The limit of viscous approximations for the equation is used to establish the existence of the global weak solution. The key elements in our analysis include a new one-sided super bound and a new higher-norm estimate on the first order derivatives of the solution. © 2013 Elsevier Inc.
Lai, S. (2013). Global weak solutions to the Novikov equation. Journal of Functional Analysis, 265(4), 520–544. https://doi.org/10.1016/j.jfa.2013.05.022