Smooth finite time singularity formation without quantization

Istvan Kadar

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arXiv · 2603.14985

Smooth finite time singularity formation without quantization

Istvan Kadar

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Abstract

We revisit the finite time singularity formation of Krieger-Schlag-Tataru [KST09] for the focusing energy critical wave equation in $\mathbb{R}^{3+1}$ from a geometric singular-analytic point of view, following Hintz [Hintz23]. We construct $C^{\nu/2-}$ regular approximate solutions that settle down to multiple solitons, shrinking at a rate $t^{\nu}$ with $\nu>1$, and approaching the origin on different geodesics $\{x=zt\}$. By fine tuning the velocities, sizes and signs of the solitons, we are able to construct smooth ans\"atze with any $\nu>8$. Using robust energy estimates, the ans\"atze are corrected to exact solutions.

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Istvan Kadar. 2026-03-16. Smooth finite time singularity formation without quantization. https://arxiv.org/abs/2603.14985

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