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- W2023782882 abstract "Results of Struwe, Grillakis, Struwe-Shatah, Kapitanski, Bahouri-Shatah, Bahouri-G'erard and Nakanishi have established global wellposedness, regularity, and scattering in the energy class for the energy-critical nonlinear wave equation $Box u = u^5$ in $R^{1+3}$, together with a spacetime bound $$ | u |_{L^4_t L^{12}_x(R^{1+3})} leq M(E(u))$$ for some finite quantity M(E(u)) depending only on the energy E(u) of u. We reprove this result, and show that this quantity obeys a bound of at most exponential type in the energy, and specifically $M(E) leq C (1+E)^{C E^{105/2}}$ for some absolute constant C > 0. The argument combines the quantitative local potential energy decay estimates of these previous papers with arguments used by Bourgain and the author for the analogous nonlinear Schrodinger equation." @default.
- W2023782882 created "2016-06-24" @default.
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- W2023782882 date "2006-01-09" @default.
- W2023782882 modified "2023-09-27" @default.
- W2023782882 title "Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions" @default.
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