The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions
Killip R, Vişan M. 2011. The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions. Proceedings of the American Mathematical Society. 139(5), 1805–1817.
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Author
Killip, Rowan;
Vişan, MonicaISTA
Abstract
We consider the defocusing nonlinear wave equation utt − Δu +
|u|
pu = 0 with spherically-symmetric initial data in the regime 4
d−2 <p< 4
d−3
(which is energy-supercritical) and dimensions 3 ≤ d ≤ 6; we also consider
d ≥ 7, but for a smaller range of p> 4
d−2 . The principal result is that
blowup (or failure to scatter) must be accompanied by blowup of the critical
Sobolev norm. An equivalent formulation is that maximal-lifespan solutions
with bounded critical Sobolev norm are global and scatter
Mathematics Subject Classification
Publishing Year
Date Published
2011-05-01
Journal Title
Proceedings of the American Mathematical Society
Publisher
American Mathematical Society
Volume
139
Issue
5
Page
1805-1817
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Vişan M. The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions. Proceedings of the American Mathematical Society. 2011;139(5):1805-1817. doi:10.1090/s0002-9939-2010-10615-9
Killip, R., & Vişan, M. (2011). The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/s0002-9939-2010-10615-9
Killip, Rowan, and Monica Vişan. “The Radial Defocusing Energy-Supercritical Nonlinear Wave Equation in All Space Dimensions.” Proceedings of the American Mathematical Society. American Mathematical Society, 2011. https://doi.org/10.1090/s0002-9939-2010-10615-9.
R. Killip and M. Vişan, “The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions,” Proceedings of the American Mathematical Society, vol. 139, no. 5. American Mathematical Society, pp. 1805–1817, 2011.
Killip R, Vişan M. 2011. The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions. Proceedings of the American Mathematical Society. 139(5), 1805–1817.
Killip, Rowan, and Monica Vişan. “The Radial Defocusing Energy-Supercritical Nonlinear Wave Equation in All Space Dimensions.” Proceedings of the American Mathematical Society, vol. 139, no. 5, American Mathematical Society, 2011, pp. 1805–17, doi:10.1090/s0002-9939-2010-10615-9.
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