Abstract
We establish a kind of weighted space–time L2 estimate, which belongs to Keel–Smith–Sogge type estimates, for perturbed linear elastic wave equations in Rn(n≥3). We also apply this estimate to give an alternative and short proof for John's almost global existence theorem for 3-D nonlinear elastic waves (John 1988, [10]), and show the global existence of small smooth solutions for nonlinear elastic waves in high space dimensions n≥4.
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