A new result for the local well-posedness of the generalized Camassa-Holm equations in critial Besov spaces B^(1)/(p)_p,1,1≤ p

2022/01/23 by Tu, Xi, Yin, Zhaoyang, Guo, Yingying
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.09162

Abstract

This paper is devoted to studying the local well-posedness (existence,uniqueness and continuous dependence) for the generalized Camassa-Holm equations in critial Besov spaces B^(1)/(p)_p,1 with 1≤ p max\(1)/(2),(1)/(p)\ or s=(1)/(p), p∈[1,2], r=1 in \citelinb,tu-yin4. The main difficulty is to prove the uniqueness, which need to use the Moser-type inequality. To overcome the difficulty, we use the Lagrange coordinate transformation to obtain the uniqueness.

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