The Local Strong and Weak Solutions for a Generalized Novikov Equation

The Kato theorem for abstract differential equations is applied to establish the local well-posedness of the strong solution for a nonlinear generalized Novikov equation in space C([0,T),Hs(R))∩C1([0,T),Hs-1(R)) with s>(3/2). The existence of weak solutions for the equation in lower-order Sobolev space Hs(R) with 1≤s≤(3/2) is acquired