Advances in Mathematical Physics
Volume 2013 (2013), Article ID 810725, 11 pages
http://dx.doi.org/10.1155/2013/810725
Research Article

On the Cauchy Problem for the Two-Component Novikov Equation

Yongsheng Mi,1,2 Chunlai Mu,1 and Weian Tao2

1College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China
2College of Mathematics and Computer Sciences, Yangtze Normal University, Chongqing, Fuling 408100, China

Received 9 January 2013; Accepted 27 March 2013

Academic Editor: M. Lakshmanan

Copyright © 2013 Yongsheng Mi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We are concerned with the Cauchy problem of two-component Novikov equation, which was proposed by Geng and Xue (2009). 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 Danchin's cerebrated paper (2001). 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 Himonas (2003) to more general equations.