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 u 0 ∈ H s ( s > 3 2 ) 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 H q ( R ) space with 0 ≤ q ≤ 1 2 , which are derived from the equation itself, are developed to prove the existence and uniqueness of the global weak solutions.