| Abstract: |
| 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 $C^\alpha$ vorticities not necessarily vanishing on the boundary with any $0<\alpha<1$, and establish finite-time singularity formation within the same class for smooth and compactly supported initial data. |
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