A new result for the local well-posedness of the generalized Camassa-Holm equations in critial Besov spaces $B_{p,1}^{\frac{1}{p}},1\le p<+\infty$

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 $B_{p,1}^{\frac{1}{p}}$ with $1\le p<+\infty$, which improves the previous index $s>\max \{\frac{1}{2},\frac{1}{p}\}$ or $s=\frac{1}{p},p\in [1,2],r=1$ in \cite{linb,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.

13 pages. arXiv admin note: text overlap with arXiv:2101.00803