论文标题
对于不可压缩的Euler方程的轴对称爆破解决方案的不稳定性
Instability for Axisymmetric Blow-up Solutions to Incompressible Euler Equations
论文作者
论文摘要
尚不清楚是否可以在有限的时间内对不可压缩的Euler方程进行解决方程。在[{\ em comm。数学。 Phys。}，378：557--568，2020]，已经表明，如果存在，则这种解决方案将在接近爆破的时间内线性不稳定。在本文中，我们表明，即使在更刚性的轴对称情况下，同样的现象也存在。为了获得此结果，我们首先证明仅涉及涡度的环形成分的爆破标准。还研究了爆破轮廓的不稳定性。
It is still not known whether a solution to the incompressible Euler equation, endowed with a smooth initial value, can blow-up in finite time. In [{\em Comm. Math. Phys.}, 378:557--568, 2020] it has been shown that, if it exists, such a solution becomes linearly unstable close to the blow-up time. In this paper, we show that the same phenomenon holds even in the more rigid axisymmetric case. To obtain this result, we first prove a blow-up criterion involving only the toroidal component of the vorticity. The instability of blow-up profiles is also investigated.
