论文标题
关于轴对称的规律性，在四个和更高维
On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions
论文作者
论文摘要
在本文中，我们考虑了四个和更高维度的Euler方程的轴对称，无漩涡的溶液。我们表明，在尺寸中$ d \ geq 4 $，轴对称，无漩涡的欧拉方程解决方案具有属性，可以允许在$ d = 3 $时排除形式的有限时间奇点形成，并且我们证明，我们证明了对eulere euler euler equeration in dememension in demension in dememension nidemention $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d \ de的有条件爆炸结果。必须在解决方案上施加的条件，以暗示爆炸变得较弱，因为$ d \ to +\ infty $，表明随着尺寸的增加，动态变得更加单数。
In this paper, we consider axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions. We show that in dimension $d\geq 4$, axisymmetric, swirl-free solutions of the Euler equation have properties which could allow finite-time singularity formation of a form that is excluded when $d=3$, and we prove a conditional blowup result for axisymmetric, swirl-free solutions of the Euler equation in dimension $d\geq 4$. The condition which must be imposed on the solution in order to imply blowup becomes weaker as $d\to +\infty$, suggesting the dynamics are becoming much more singular as the dimension increases.
