Non-uniform Dependence on Initial Data for the Camassa–Holm Equation in the Critical Besov Space

Whether or not the data-to-solution map of the Cauchy problem for the Camassa–Holm equation and Novikov equation in the critical Besov space B 2 , 1 3 / 2 ( R ) is uniformly continuous remains open. In the paper, we aim at solving the open question left in the previous works (Li et al. in J Differ E...

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Published inJournal of mathematical fluid mechanics Vol. 23; no. 2
Main Authors Li, Jinlu, Wu, Xing, Yu, Yanghai, Zhu, Weipeng
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2021
Springer Nature B.V
Subjects
Cauchy problems
Classical and Continuum Physics
Fluid mechanics
Fluid- and Aerodynamics
Function space
Mathematical Methods in Physics
Physics
Physics and Astronomy
Theoretical mathematics
Camassa–Holm (Novikov) equation
Non-uniform continuous dependence
76W05
35Q35
35A01
Critical Besov spaces
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Summary:Whether or not the data-to-solution map of the Cauchy problem for the Camassa–Holm equation and Novikov equation in the critical Besov space B 2 , 1 3 / 2 ( R ) is uniformly continuous remains open. In the paper, we aim at solving the open question left in the previous works (Li et al. in J Differ Equ 269:8686–8700, 2020a; J Math Fluid Mech 22:50, 2020b) and giving a negative answer to this problem.
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ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-021-00571-5