The existence of global strong and weak solutions for the Novikov equation

The well-posedness of the global strong and weak solutions for the Novikov equation is investigated. Provided that initial value u0∈Hs(s>32) and satisfying a sign condition, the existence and uniqueness of global strong solutions for the equation are shown to be valid in Sobolev space. The estimates in Hq(R)Hq(R) space with 0≤q≤12, which are derived from the equation itself, are developed to prove the existence and uniqueness of the global weak solutions.