The defocusing energy-supercritical nonlinear wave equation in three space dimensions
Killip R, Vişan M. 2011. The defocusing energy-supercritical nonlinear wave equation in three space dimensions. Transactions of the American Mathematical Society. 363(7), 3893–3893.
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Author
Killip, Rowan;
Vişan, MonicaISTA
Abstract
We consider the defocusing nonlinear wave equation (mathematical formular) in the energy-supercritical regime p > 4. For even values of the power p, we show that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that solutions with bounded critical Sobolev norm are global and scatter. The impetus to consider this problem comes from recent work of Kenig and Merle who treated the case of spherically-symmetric solutions.
Publishing Year
Date Published
2011-01-28
Journal Title
Transactions of the American Mathematical Society
Publisher
American Mathematical Society
Volume
363
Issue
7
Page
3893-3893
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Vişan M. The defocusing energy-supercritical nonlinear wave equation in three space dimensions. Transactions of the American Mathematical Society. 2011;363(7):3893-3893. doi:10.1090/s0002-9947-2011-05400-0
Killip, R., & Vişan, M. (2011). The defocusing energy-supercritical nonlinear wave equation in three space dimensions. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/s0002-9947-2011-05400-0
Killip, Rowan, and Monica Vişan. “The Defocusing Energy-Supercritical Nonlinear Wave Equation in Three Space Dimensions.” Transactions of the American Mathematical Society. American Mathematical Society, 2011. https://doi.org/10.1090/s0002-9947-2011-05400-0.
R. Killip and M. Vişan, “The defocusing energy-supercritical nonlinear wave equation in three space dimensions,” Transactions of the American Mathematical Society, vol. 363, no. 7. American Mathematical Society, pp. 3893–3893, 2011.
Killip R, Vişan M. 2011. The defocusing energy-supercritical nonlinear wave equation in three space dimensions. Transactions of the American Mathematical Society. 363(7), 3893–3893.
Killip, Rowan, and Monica Vişan. “The Defocusing Energy-Supercritical Nonlinear Wave Equation in Three Space Dimensions.” Transactions of the American Mathematical Society, vol. 363, no. 7, American Mathematical Society, 2011, pp. 3893–3893, doi:10.1090/s0002-9947-2011-05400-0.
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