Ill-posedness for the higher dimensional Camassa-Holm equations in Besov spaces

2021/06/01 by Li, Min, Guo, Yingying
#35A01 #35Q35 #37K10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.00540

Abstract

In the paper, by constructing a initial data u₀∈ B^σ_p,∞ with σ-2>max\1+\frac 1 p, \frac 3 2\, we prove that the corresponding solution to the higher dimensional Camassa-Holm equations starting from u₀ is discontinuous at t=0 in the norm of B^σ_p,∞, which implies that the ill-posedness for the higher dimensional Camassa-Holm equations in B^σ_p,∞.

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