In this paper, we mainly study the Cauchy problem of the Novikov equation. We first establish the local well-posedness and give the precise blow-up scenario for the equation. Then we show that the equation has smooth solutions which exist globally in time. Finally we prove that peakon solutions to the equation are global weak solutions.

@article{ASNSP_2012_5_11_3_707_0, author = {Wu, Xinglong and Yin, Zhaoyang}, title = {Well-posedness and global existence for the Novikov equation}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {3}, year = {2012}, pages = {707-727}, zbl = {1261.35041}, mrnumber = {3059842}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2012_5_11_3_707_0} }

Wu, Xinglong; Yin, Zhaoyang. Well-posedness and global existence for the Novikov equation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 3, pp. 707-727. http://www.numdam.org/item/ASNSP_2012_5_11_3_707_0/

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