A note on the Cauchy problem for the periodic two-component Novikov system. Issue 6 (25th April 2020)

• Record Type: Journal Article
• Authors: Wang, Haiquan; Fu, Ying
• Is Part Of: Applicable analysis. Volume 99:Issue 6(2020)
• Page Start: 1042
• Page End: 1065
• Publication Date: 2020-04-25
• Subjects: Adrian Constantin; The periodic two-component Novikov system -- approximate solutions -- Besov spaces; 35B30 -- 35G25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1520981
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: Considered herein is the initial value problem for the periodic two-component Novikov system. It is shown that the solution map of this problem is not uniformly continuous in Besov spaces B 2, r s ( T ) × B 2, r s − 1 ( T ) with s > 3 / 2, 1 ≤ p < ∞ . Furthermore, the non-uniform continuous dependence on initial data is established in Besov space B 2, 1 3 / 2 ( T ) × B 2, 1 1 / 2 ( T ) . Based on the well-posedness result and the lifespan for this problem, the method of approximate solutions is utilized.