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

Thomas Duyckaerts; Giuseppe Negro

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

Analysis of PDEs 2024-02-06 v2

Authors: Thomas Duyckaerts , Giuseppe Negro

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.

Keywords

cubic wave equation global solutions self-similar behaviour scattering finite-time blow-up threshold behaviour

Cite

@article{arxiv.2304.09567,
  title  = {Global solutions with asymptotic self-similar behaviour for the cubic wave equation},
  author = {Thomas Duyckaerts and Giuseppe Negro},
  journal= {arXiv preprint arXiv:2304.09567},
  year   = {2024}
}

Comments

41 pages, 7 figures. v2: referee suggestions incorporated. To appear in Communications in Mathematical Physics

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