Nonuniform Dependence of a Two-Component NOVIKOV System in Besov Spaces

Nonuniform Dependence of a Two-Component NOVIKOV System in Besov Spaces

Considered herein is the Cauchy problem of the two-component Novikov system. In the periodic case, we first constructed an approximate solution sequence that possesses the nonuniform dependence property; then, by applying the energy methods, we managed to prove that the difference between the approx...

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Veröffentlicht in:Mathematics (Basel) 2023-04, Vol.11 (9), p.2041
Hauptverfasser: Yu, Shengqi, Liu, Jie
Format: Artikel
Sprache:eng
Schlagworte:
Cauchy problem
Cauchy problems
critical Besov spaces
Energy methods
Estimates
Frequency analysis
Function space
Investigations
Mathematical research
Metric spaces
non-uniform dependence
Partial differential equations
Sequences (Mathematics)
Shallow water equations
supercritical Besov spaces
two-component Novikov system
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Zusammenfassung:Considered herein is the Cauchy problem of the two-component Novikov system. In the periodic case, we first constructed an approximate solution sequence that possesses the nonuniform dependence property; then, by applying the energy methods, we managed to prove that the difference between the approximate and actual solution is negligible, thus succeeding in proving the nonuniform dependence result in both supercritical Besov spaces Bp,rs(T)×Bp,rs(T) with s>max{32,1+1p},1≤p≤∞,1≤rmax{32,1+1p},1≤p≤∞,1≤r
ISSN:2227-7390
2227-7390
DOI:10.3390/math11092041