论文标题
novikov方程在关键的besov空间中的不适性$ b^{1} _ {\ infty，1}（\ mathbb {r}）$
Ill-posedness of the Novikov equation in the critical Besov space $B^{1}_{\infty,1}(\mathbb{R})$
论文作者
论文摘要
结果表明，Camassa-Holm和Novikov方程式在$ b_ {p，r}^{1+1/p}（\ Mathbb {r}）$中，带有$（p，p，r）\ in [1，\ infty] \ times（1，\ infty] \ times（1，\ infty] in \ cite in \ cite in \ cite in \ cite {guo2019} $ b_ {p，1}^{1+1/p}（\ mathbb {r}）$，in \ cite {ye}中的$ p \ in [1，\ infty）$ in [1，\ infty）$。最近，在\ cite {guo}中证明了$ b^{1} _ {\ mathbb {r}）$的Camassa-Holm方程的不良性。在本文中，我们将解决Novikov方程的唯一左端点情况$ r = 1 $。更确切地说，我们通过展示norm unflation现象，证明了$ b^{1} _ {\ mathbb {r}）$中Novikov方程的不良性。
It is shown that both the Camassa-Holm and Novikov equations are ill-posed in $B_{p,r}^{1+1/p}(\mathbb{R})$ with $(p,r)\in[1,\infty]\times(1,\infty]$ in \cite{Guo2019} and well-posed in $B_{p,1}^{1+1/p}(\mathbb{R})$ with $p\in[1,\infty)$ in \cite{Ye}. Recently, the ill-posedness for the Camassa-Holm equation in $B^{1}_{\infty,1}(\mathbb{R})$ has been proved in \cite{Guo}. In this paper, we shall solve the only left an endpoint case $r=1$ for the Novikov equation. More precisely, we prove the ill-posedness for the Novikov equation in $B^{1}_{\infty,1}(\mathbb{R})$ by exhibiting the norm inflation phenomena.
