论文标题
关于cauchy问题的问题，对于临界空间中的弱耗散的camassa-holm方程
On the Cauchy problem for a weakly dissipative Camassa-Holm equation in critical Besov spaces
论文作者
论文摘要
在本文中，我们主要考虑了较弱的Camassa-Holm方程的库奇问题。我们首先在besov空间中建立本地方程式$ b^{s} _ {p，r} $，其中$ s> 1+ \ frac 1 p $和$ s = 1+\ frac 1 p，r = 1，r = 1，p \ in [1，\ infty）。最后，我们获得了两个爆炸结果，可用于在关键空间中造成不良的证明。
In this paper, we mainly consider the Cauchy problem of a weakly dissipative Camassa-Holm equation. We first establish the local well-posedness of equation in Besov spaces $B^{s}_{p,r}$ with $s>1+\frac 1 p$ and $s=1+\frac 1 p , r=1,p\in [1,\infty).$ Then, we prove the global existence for small data, and present two blow-up criteria. Finally, we get two blow-up results, which can be used in the proof of the ill-posedness in critical Besov spaces.
