L²-blowup estimates of the plate equation

2021/12/14 by Ikehata, Ryo
#35B40 #35C20 #35L05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2112.07142

Abstract

We consider the Cauchy problems in n-dimensional Euclidean space for the plate equation with a weighted L¹-initial data. We derive optimal estimates of the L²-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.

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