The incompressible Euler equations under octahedral symmetry: Singularity formation in a fundamental domain
The incompressible Euler equations under octahedral symmetry: Singularity formation in a fundamental domain
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DOI：
10.1016/j.aim.2021.108091
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发表时间：
2020-01
影响因子：
1.7
通讯作者：
T. Elgindi;In-Jee Jeong
中科院分区：
文献类型：
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作者：
T. Elgindi;In-Jee Jeong
我们考虑八面体对称群的涡量型三维不可压缩欧拉方程：{(x 1, x 2, x 3): 0< x 3< x 2< x 1}。在此范围内，我们证明了C α涡旋在任意0< α< 1的边界上不一定消失的局部适定性，并建立了光滑紧支持初始数据在同一类内的有限时间奇点形成。通过一系列的反射，我们可以将解推广到所有的r3，从而得到具有有界和分段光滑涡度的三维欧拉方程在r3中的有限时间奇点形成。
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 R 3 via a sequence of reflections, and therefore we obtain finite-time singularity formation for the 3D Euler equations in R 3 with bounded and piecewise smooth vorticities.