On Morawetz estimates for the elastic wave equation

Abstract

We establish Morawetz-type estimates for solutions to the elastic wave equation with singular weights of the form $|x{|}^{-\hat{I}\pm }$ or $|(x,t){|}^{-\hat{I}\pm }$. In particular, we show that space-time weights $|(x,t){|}^{-\hat{I}\pm }$ admit stronger singularities and require weaker regularity assumptions on the initial data compared to purely spatial weights $|x{|}^{-\hat{I}\pm }$.

To appear in Anal. Math. Phys., 15 pages