The Local Strong and Weak Solutions for a Generalized Novikov Equation

Abstract

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