Global weak solutions for the Novikov equation

In the paper, we mainly study the existence and uniqueness of global weak solutions for the Novikov equation. We first recall some results and definitions on strong solutions and weak solutions for the equation. Then, we show that the equation has smooth solutions which exist globally in time, provided the initial data satisfy certain sign conditions. Finally we prove the existence and uniqueness of global weak solutions to the equation with the initial data satisfying certain sign conditions.