论文标题
在besov空间中的两_component novikov系统的ill_poseentes
Ill_posedness for a two_component Novikov system in Besov space
论文作者
论文摘要
在本文中，我们考虑了这条线上两个组件的Novikov系统的Cauchy问题。由$ b_ {p，\ infty}^{s-1}（\ Mathbb {r}）\ times b_ {p，\ infty}^s（\ infty}^s（\ mathbb {r}）$ at $ b_ { \ frac {5} {2} \} $和$ 1 \ leq p \ leq \ leq \ infty $，我们表明，从$（ρ_0，u_0）$开始的任何能量有限的解决方案都不会收敛到$（ρ_0，u_0，u_0，u_0）$，在$ b_ { b_ {p，\ infty}^s（\ mathbb {r}）$作为零，从而导致数据到解决方案的映射和不适当的不连续性。
In this paper, we consider the Cauchy problem for a two-component Novikov system on the line. By specially constructed initial data $(ρ_0, u_0)$ in $B_{p, \infty}^{s-1}(\mathbb{R})\times B_{p, \infty}^s(\mathbb{R})$ with $s>\max\{2+\frac{1}{p}, \frac{5}{2}\}$ and $1\leq p \leq \infty$, we show that any energy bounded solution starting from $(ρ_0, u_0)$ does not converge back to $(ρ_0, u_0)$ in the metric of $B_{p, \infty}^{s-1}(\mathbb{R})\times B_{p, \infty}^s(\mathbb{R})$ as time goes to zero, thus results in discontinuity of the data-to-solution map and ill-posedness.
