Expanding-ring conjecture for the post-singularity set

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Let T∗T_* be the singularity time and let (r,x3)(r,x_3) be axisymmetric coordinates. Define

S(t)={(r,x3)=(δ(t),0)}.\mathcal{S}(t)=\{(r,x_3)=(\delta(t),0)\}.

Expanding-ring conjecture. The singular set of the solutions of the cited self-similar Euler construction propagates within the natural symmetry class as the expanding ring S(t)\mathcal{S}(t), where δ(T∗)=0\delta(T_*)=0 and δ\delta is increasing in tt for every t≥T∗t\geq T_*. The statement concerns the continuation of the singular set after blow-up and remains open.

References

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).

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