Ill-posedness for the two component Degasperis-Procesi equation in critical Besov space

2022/04/29 by Li, Jinlu, Li, Min, Zhu, Weipeng
#35Q53 #37K10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.14151

Abstract

In this paper, we study the Cauchy problem for the two component Degasperis-Procesi equation in critical Besov space B¹_∞,1(\mathbb R). By presenting a new construction of initial data, we proved the norm inflation of the corresponding solutions in B¹_∞,1(\mathbb R) and hence ill-posedness. This is quite different from the local well-posedness result for the Degasperis-Procesi equation in critical Besov space B¹_∞,1(\mathbb R) due to the coupled structure of density function.

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