论文标题
八面体对称下的不可压缩的欧拉方程：基本域中的奇异性形成
The incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domain
论文作者
论文摘要
我们在以下基本域中以涡流对称组的以下基本域中考虑3D不可压缩的Euler方程：$ \ {（x_1，x_2，x_3）：0 <x_3 <x_3 <x_2 <x_2 <x_1 \ \}。 $ 0 <α<1 $，并在同一类中建立有限的时间奇异性形成，以平滑而紧凑的初始数据。解决方案可以通过一系列反射序列扩展到所有$ \ mathbb {r}^3 $，因此，我们在$ \ mathbb {r}^3 $中获得3D Euler方程的有限时间奇异性形成，并带有有界和分段的平滑涡流。
We consider the 3D incompressible Euler equations in vorticity form in the following fundamental domain for the octahedral symmetry group: $\{ (x_1,x_2,x_3): 0<x_3<x_2<x_1 \}.$ In this domain, we prove local well-posedness for $C^α$ vorticities not necessarily vanishing on the boundary with any $0<α<1$, and establish finite-time singularity formation within the same class for smooth and compactly supported initial data. The solutions can be extended to all of $\mathbb{R}^3$ via a sequence of reflections, and therefore we obtain finite-time singularity formation for the 3D Euler equations in $\mathbb{R}^3$ with bounded and piecewise smooth vorticities.
