Ill_posedness for a two_component Novikov system in Besov space

2022/02/13 by Desheng Wu, Min Li, Wu, Xing +1
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2202.06304

openalex publication_date 2022/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the Cauchy problem for a two-component Novikov system on the line. By specially constructed initial data (ρ₀, u₀) in B_{p, ∞}^s-1(ℝ)× B_{p, ∞}^s(ℝ) with s>max\2+(1)/(p), (5)/(2)\ and 1≤ p ≤ ∞, we show that any energy bounded solution starting from (ρ₀, u₀) does not converge back to (ρ₀, u₀) in the metric of B_{p, ∞}^s-1(ℝ)× B_{p, ∞}^s(ℝ) as time goes to zero, thus results in discontinuity of the data-to-solution map and ill-posedness.

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