Blowup behaviour for the nonlinear Klein-Gordon equation
Killip R, Stovall B, Vişan M. 2014. Blowup behaviour for the nonlinear Klein-Gordon equation. Mathematische Annalen. 358(1–2), 289–350.
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Author
Killip, Rowan;
Stovall, Betsy;
Vişan, MonicaISTA
Abstract
We analyze the blowup behaviour of solutions to the focusing nonlinear Klein–Gordon equation in spatial dimensions d>=2. We obtain upper bounds on the blowup rate, both globally in space and in light cones. The results are sharp in the conformal and sub-conformal cases. The argument relies on Lyapunov functionals derived from the dilation identity. We also prove that the critical Sobolev norm diverges near the blowup time.
Publishing Year
Date Published
2014-02-01
Journal Title
Mathematische Annalen
Publisher
Springer Nature
Volume
358
Issue
1-2
Page
289-350
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Stovall B, Vişan M. Blowup behaviour for the nonlinear Klein-Gordon equation. Mathematische Annalen. 2014;358(1-2):289-350. doi:10.1007/s00208-013-0960-z
Killip, R., Stovall, B., & Vişan, M. (2014). Blowup behaviour for the nonlinear Klein-Gordon equation. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-013-0960-z
Killip, Rowan, Betsy Stovall, and Monica Vişan. “Blowup Behaviour for the Nonlinear Klein-Gordon Equation.” Mathematische Annalen. Springer Nature, 2014. https://doi.org/10.1007/s00208-013-0960-z.
R. Killip, B. Stovall, and M. Vişan, “Blowup behaviour for the nonlinear Klein-Gordon equation,” Mathematische Annalen, vol. 358, no. 1–2. Springer Nature, pp. 289–350, 2014.
Killip R, Stovall B, Vişan M. 2014. Blowup behaviour for the nonlinear Klein-Gordon equation. Mathematische Annalen. 358(1–2), 289–350.
Killip, Rowan, et al. “Blowup Behaviour for the Nonlinear Klein-Gordon Equation.” Mathematische Annalen, vol. 358, no. 1–2, Springer Nature, 2014, pp. 289–350, doi:10.1007/s00208-013-0960-z.
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