论文标题
在BESOV空间中的两个组件B家族系统的初始数据上的不均匀连续性
Non-uniform continuity on initial data for the two-component b-family system in Besov space
论文作者
论文摘要
在本文中，我们考虑了两个组件B家族系统的库奇问题，其中包括两个组件的Camassa-Holm系统和两个组件的Degasperis-Procesi系统。结果表明，在besov空间的初始数据$ b_ {p，r}^{s-1}（\ mathbb {r}）\ times b_ { \ frac {3} {2} \} $，$ 1 \ leq p，r <\ infty $。我们的结果涵盖并扩展了Sobolev空间中的先前的非均匀连续性$ H^{s-1}（\ Mathbb {r}）\ Times H^S（\ Mathbb {r}）$ for $ s> \ frac {5} {2} {2} {2} {2} $（nonlinear Anal。
In this paper, we consider the Cauchy problem of a two-component b-family system, which includes the two-component Camassa-Holm system and the two-component Degasperis-Procesi system. It is shown that the solution map of the two-component b-family system is not uniformly continuous on the initial data in Besov spaces $B_{p, r}^{s-1}(\mathbb{R})\times B_{p, r}^s(\mathbb{R})$ with $s>\max\{1+\frac{1}{p}, \frac{3}{2}\}$, $1\leq p, r< \infty$. Our result covers and extends the previous non-uniform continuity in Sobolev spaces $H^{s-1}(\mathbb{R})\times H^s(\mathbb{R})$ for $s>\frac{5}{2}$ (Nonlinear Anal., 2014) to Besov spaces.
