论文标题
关键BESOV空间中两个组件deaSperis-procesi方程的不良适应性
Ill-posedness for the two component Degasperis-Procesi equation in critical Besov space
论文作者
论文摘要
在本文中，我们研究了关键besov空间中两个组件degasperis-procesi方程的凯奇问题$ b^1 _ {\ infty，1}（\ mathbb r）$。通过提出新的初始数据结构，我们证明了$ b^1 _ {\ infty，1}（\ Mathbb r）$中相应解决方案的规范通货膨胀，从而使不足。由于密度函数的耦合结构，这与关键BESOV空间中的Degasperis-Procesi方程的局部良好性结果完全不同。
In this paper, we study the Cauchy problem for the two component Degasperis-Procesi equation in critical Besov space $B^1_{\infty,1}(\mathbb R)$. By presenting a new construction of initial data, we proved the norm inflation of the corresponding solutions in $B^1_{\infty,1}(\mathbb R)$ and hence ill-posedness. This is quite different from the local well-posedness result for the Degasperis-Procesi equation in critical Besov space $B^1_{\infty,1}(\mathbb R)$ due to the coupled structure of density function.
