On Morawetz estimates for the elastic wave equation

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

💡 Research Summary

The paper investigates Morawetz‑type weighted $L^{2}$ estimates for solutions of the elastic wave equation in $\mathbb{R}^{n}$, focusing on two families of singular weights: purely spatial weights $|x|^{-\alpha}$ and space‑time weights $|(x,t)|^{-\alpha}$. The elastic system is \