Artificial-boundary conjecture for axisymmetric Euler blow-up
Artificial-boundary conjecture for axisymmetric Euler blow-up
Consider smooth axisymmetric Euler solutions in the axisymmetric coordinate formulation, with vorticity non-vanishing on the axis of symmetry. Artificial-boundary conjecture. There exist such smooth solutions that become singular in finite time. The source explains that these solutions need not lift to smooth three-dimensional solutions on the symmetry axis, so the axis acts as an artificial boundary; the conjecture remains open.
Sources & referencesView supporting material
Primary source
Theodore D. Drivas and Tarek M. Elgindi, “Singularity formation in the incompressible Euler equation in finite and infinite time”, arXiv:2203.17221 (2022).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.