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arXiv · 2304.09567

Global solutions with asymptotic self-similar behaviour for the cubic wave equation

Thomas Duyckaerts·Giuseppe Negro
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Abstract

We construct a two-parameter family of explicit solutions to the cubic wave equation on $\mathbb{R}^{1+3}$. Depending on the value of the parameters, these solutions either scatter to linear, blow-up in finite time, or exhibit a new type of threshold behaviour which we characterize precisely.

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Thomas Duyckaerts, Giuseppe Negro. 2023-04-19. Global solutions with asymptotic self-similar behaviour for the cubic wave equation. https://arxiv.org/abs/2304.09567

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