Ill-Posedness of a Three-Component Novikov System in Besov Spaces

Shengqi Yu () and Lin Zhou
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Shengqi Yu: School of Mathematics and Statistics, Nantong University, Nantong 226007, China
Lin Zhou: School of Mathematics and Statistics, Nantong University, Nantong 226007, China

Mathematics, 2024, vol. 12, issue 9, 1-15

Abstract: In this paper, we consider the Cauchy problem for a three-component Novikov system on the line. We give a construction of the initial data ( ρ 0 , u 0 , v 0 ) ∈ B p , ∞ σ − 1 ( R ) × B p , ∞ σ ( R ) × B p , ∞ σ ( R ) with σ > max 3 + 1 p , 7 2 , 1 ≤ p ≤ ∞ , such that the corresponding solution to the three-component Novikov system starting from ( ρ 0 , u 0 , v 0 ) is discontinuous at t = 0 in the metric of B p , ∞ σ − 1 ( R ) × B p , ∞ σ ( R ) × B p , ∞ σ ( R ) , which implies the ill-posedness for this system in B p , ∞ σ − 1 ( R ) × B p , ∞ σ ( R ) × B p , ∞ σ ( R ) .

Keywords: ill-posedness; three-component Novikov system; Besov spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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