Publications [#361921] of Tarek M Elgindi

Papers Published

1. Elgindi, TM; Jeong, IJ, The incompressible Euler equations under octahedral symmetry: Singularity formation in a fundamental domain, Advances in Mathematics, vol. 393 (December, 2021) [doi]
   (last updated on 2026/01/21)

   Abstract:
   We consider the 3D incompressible Euler equations in vorticity form in the following fundamental domain for the octahedral symmetry group: {(x1,x2,x3):0321}. 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 R³ via a sequence of reflections, and therefore we obtain finite-time singularity formation for the 3D Euler equations in R³ with bounded and piecewise smooth vorticities.