L²-Blowup Estimates of the Plate Equation

Abstract

We consider the Cauchy problems in Rⁿ for the plate equation with a weighted L¹-initial data. We derive new optimal estimates of the L²-norm of solutions for n = 1,2,3,4. In particular, such obtained results express infinite time blowup property in the case when the 0-th moment of the initial velocity does not vanish. From a series of estimates obtained in this paper one can observe much complicated growth properties of the solution itself of the plate equations.