L^{2}-blowup estimates of the plate equation

Abstract

We consider the Cauchy problems in n-dimensional Euclidean space for the plate equation with a weighted L^{1}-initial data. We derive optimal estimates of the L^{2}-norm of solutions for n = 1, 2, 3, 4. In particular, such obtained results express infinite time blowup properties in the case when the 0-th moment of the initial velocity does not vanish. The idea to derive them is strongly inspired from an already developed technique by the author's collaborative works.