Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data

Kotaro Hisa; Jin Takahashi; Erbol Zhanpeisov

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arXiv · 2604.20396

Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data

Kotaro Hisa·Jin Takahashi·Erbol Zhanpeisov

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Abstract

We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions that decay strictly more slowly than the self-similar rate. Moreover, the blow-up and decay rates are not uniquely determined by the decay rate of the initial data, but exhibit a certain flexibility depending on the construction. The proof is based on gluing suitably rescaled bubbles to forward self-similar solutions.

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Kotaro Hisa, Jin Takahashi, Erbol Zhanpeisov. 2026-04-22. Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data. https://arxiv.org/abs/2604.20396

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