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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.
Wu, Xinglong 1 ; Yin, Zhaoyang 1
@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},
pages = {707--727},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 11},
number = {3},
year = {2012},
mrnumber = {3059842},
zbl = {1261.35041},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_3_707_0/}
}
TY - JOUR AU - Wu, Xinglong AU - Yin, Zhaoyang TI - Well-posedness and global existence for the Novikov equation JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 707 EP - 727 VL - 11 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_3_707_0/ LA - en ID - ASNSP_2012_5_11_3_707_0 ER -
%0 Journal Article %A Wu, Xinglong %A Yin, Zhaoyang %T Well-posedness and global existence for the Novikov equation %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 707-727 %V 11 %N 3 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_3_707_0/ %G en %F 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, Série 5, Tome 11 (2012) no. 3, pp. 707-727. http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_3_707_0/