Multi‐bubble blowup of focusing energy‐critical wave equation in dimension 6

We consider the energy‐critical focusing wave equation ∂t2u(t,x)−Δu(t,x)=u(t,x)u(t,x),t∈ℝ,x∈ℝ6, and we prove the existence of infinite time blowup at the vertices of any regular polyhedron. The blowup rate of each bubble is asymptotic to ckt−1 as t goes to +∞, where the constants ck depend on the di...

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Veröffentlicht in:Mathematical methods in the applied sciences 2022-08, Vol.45 (12), p.7273-7306
Hauptverfasser: Yi, Yezhou, Zhao, Lifeng
Format: Artikel
Sprache:eng
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Zusammenfassung:We consider the energy‐critical focusing wave equation ∂t2u(t,x)−Δu(t,x)=u(t,x)u(t,x),t∈ℝ,x∈ℝ6, and we prove the existence of infinite time blowup at the vertices of any regular polyhedron. The blowup rate of each bubble is asymptotic to ckt−1 as t goes to +∞, where the constants ck depend on the distances between the vertices. This result is an add‐on to previous constructions of blowup solutions of the energy‐critical wave equation.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.8236