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 |
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Hauptverfasser: | , |
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. |
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ISSN: | 0170-4214 1099-1476 |
DOI: | 10.1002/mma.8236 |