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We consider the semi-linear, defocusing wave equation $\partial_t^2 u -\Delta u = -|u|^{p-1} u$ in $\mathbb{R}^d$ with $1+4/(d-1)\leq p < 1+4/(d-2)$.We generalize the inward/outward energy theory and weighted Morawetz estimatesin 3D to higher dimensions. As an application we show the scattering ofsolutions if the energy of initial data decays at a certain rate as $|x|\rightarrow \infty$.

Inward/outward Energy Theory of Wave Equation in Higher Dimensions