The local strong and weak solutions for a generalized Novikov equation (Q417092)

Summary: 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 \(C([0, T), H^s(\mathbb R)) \cap C^1([0, T), H^{s-1}(\mathbb R))\) with \(s > (3/2)\). The existence of weak solutions for the equation in the lower-order Sobolev space \(H^s(\mathbb R)\) with \(1 \leq s \leq (3/2)\) is acquired.