Localized Sequential Bubbling for the Radial Energy Critical Semilinear Heat Equation
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10013_2023_Article_648.pdf
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Author(s)
Lawrie, Andrew
Date Issued
September 26, 2023
Publisher
Springer Nature Singapore
Citation
Lawrie, Andrew. 2023. "Localized Sequential Bubbling for the Radial Energy Critical Semilinear Heat Equation."
Version
Final published version
Abstract
Abstract
In this expository note, we prove a localized bubbling result for solutions of the energy critical nonlinear heat equation with bounded
$$\dot{H} ^1$$
H
˙
1
norm. The proof uses a combination of Gérard’s profile decomposition (ESAIM Control Optim. Calc. Var. 3: 213–233, 1998), concentration compactness techniques in the spirit of Duyckaerts, Kenig, and Merle’s seminal work (Geom. Funct. Anal. 22: 639–698, 2012), and a virial argument in the spirit of Jia and Kenig’s work (Amer. J. Math. 139: 1521–1603, 2017) to deduce the vanishing of the error in the neck regions between the bubbles. The argument is based closely on an analogous lemma proved in the author’s recent work with Jendrej (arXiv:2210.14963, 2022) on the equivariant harmonic map heat flow in dimension two.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s10013-023-00648-w
