论文标题
$ c^{k，β} $中的不存在和强大的不存在，用于广义的表面准地斑方程
Non-existence and strong ill-posedness in $C^{k,β}$ for the generalized Surface Quasi-geostrophic equation
论文作者
论文摘要
当速度比主动标量函数（即$γ\ in（0,1）$）时，我们将考虑通用表面准地球方程（$γ$ -SQG）的解决方案。在本文中，我们在$ c^{k，β} $（$ k \ geq 1 $，$β\ in（0,1] $和$ k+β> 1+γ$）中建立了强大的不良性，我们还以$ \ mathbb {r}^2 $构建解决方案，最初是$ c^{对于$ t> 0 $，这些解决方案留在$ h^{k+β+1-2Δ} $中，对于一些小$δ$，并且任意长时间。
We consider solutions to the generalized Surface Quasi-geostrophic equation ($γ$-SQG) when the velocity is more singular than the active scalar function (i.e. $γ\in(0,1)$). In this paper we establish strong ill-posedness in $C^{k,β}$ ($k\geq 1$, $β\in(0,1]$ and $k+β>1+γ$) and we also construct solutions in $\mathbb{R}^2$ that initially are in $C^{k,β}\cap L^2$ but are not in $C^{k,β}$ for $t>0$. Furthermore these solutions stay in $H^{k+β+1-2δ}$ for some small $δ$ and an arbitrarily long time.
