On the Cauchy problem for the two-component Novikov equation (Q1953180)

Summary: We are concerned with the Cauchy problem of two-component Novikov equation, which was proposed by \textit{X. Geng} and \textit{B. Xue} [Nonlinearity 22, No. 8, 1847--1856 (2009; Zbl 1171.37331)]. We establish the local well-posedness in a range of the Besov spaces by using Littlewood-Paley decomposition and transport equation theory which is motivated by that in \textit{R. Danchin}'s cerebrated paper [Differ. Integral Equ. 14, No. 8, 953--988 (2001; Zbl 1161.35329)]. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time, which extend some results of \textit{A. A. Himonas} and \textit{G. Misiołek} [Math. Ann. 327, No. 3, 575--584 (2003; Zbl 1073.35008)] to more general equations.