Global well-posedness for the periodic Novikov equation with cubic nonlinearity. Issue 2 (1st February 2016)

• Record Type: Journal Article
• Authors: Wu, Xinglong; Guo, Boling
• Is Part Of: Applicable analysis. Volume 95:Issue 2(2016)
• Page Start: 405
• Page End: 425
• Publication Date: 2016-02-01
• Subjects: the periodic Novikov equation -- well-posedness -- blow-up scenario -- conservation laws -- global solutions -- Peakon solutions; 35G25 -- 35L05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1005611
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper is devoted to the study of the Cauchy problem to the periodic Novikov equation. Firstly, the local well-posedness for the equation is established. Secondly, we give the precise blow-up criterion, conservation laws, and prove that the equation has global strong solutions in time, if the initial potential does not change sign on . Thirdly, with the initial potential satisfying the sign conditions, we show the existence of global weak solutions in time. Moreover, the uniqueness of global solution is addressed.