Abstract
We prove global existence of smooth solutions of the 3D log-log energy-supercritical wave equation
with and smooth initial data . First we control the norm of the solution on an arbitrary size time interval by an expression depending on the energy and an a priori upper bound of its norm, with . The proof of this long time estimate relies upon the use of some potential decay estimates and a modification of an argument by Tao. Then we find an a posteriori upper bound of the norm of the solution by combining the long time estimate with an induction on time of the Strichartz estimates.
Citation
Tristan Roy. "Global existence of smooth solutions of a 3D log-log energy-supercritical wave equation." Anal. PDE 2 (3) 261 - 280, 2009. https://doi.org/10.2140/apde.2009.2.261
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