论文标题
$ \ mathbb {r}^{d} $中的某些轴对称Euler流动的全局规律性
Global regularity for some axisymmetric Euler flows in $\mathbb{R}^{d}$
论文作者
论文摘要
我们认为轴对称欧拉在$ \ mathbb {r}^{d} $带有$ d \ geq 4 $中没有旋流的情况下，对于这是一个空意的解决方案的全局规律性是一个开放的问题。当$ d = 4 $时，我们在假设初始涡度可以满足无穷大的某些衰减并在轴上消失的假设获得全球规律性。假设最初的涡度是一个标志，则可以保证$ d \ leq 7 $的全球规律性。
We consider axisymmetric Euler flows without swirl in $\mathbb{R}^{d}$ with $d\geq 4$, for which the global regularity of smooth solutions is an open problem. When $d = 4$, we obtain global regularity under the assumption that the initial vorticity satisfies some decay at infinity and is vanishing at the axis. Assuming further that the initial vorticity is of one sign guarantees global regularity for $d\leq 7$.
