L2-blowup estimates of the wave equation and its application to local energy decay.

We consider the Cauchy problems in R n for the wave equation with a weighted L 1 -initial data. We derive sharp infinite time blowup estimates of the L 2 -norm of solutions in the case of n = 1 and n = 2. Then, we apply it to the local energy decay estimates for n = 2 , which is not studied so completely when the 0 th moment of the initial velocity does not vanish. The idea to derive them is strongly inspired from a technique used in [R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Differ. Equ. 257 (2014) 2159–2177; R. Ikehata and M. Onodera, Remarks on large time behavior of the L 2 -norm of solutions to strongly damped wave equations, Differ. Integral Equ. 30 (2017) 505–520]. [ABSTRACT FROM AUTHOR]