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The topic of this paper is a semi-linear, energy sub-critical, defocusingwave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensionalspace with $3\leq p<5$. We generalize inward/outward energy theory and weightedMorawetz estimates for radial solutions to the non-radial case. As anapplication we show that if $3<p<5$ and $\kappa>\frac{5-p}{2}$, then thesolution scatters as long as the initial data $(u_0,u_1)$ satisfy  \[  \int_{{\mathbb R}^3} (|x|^\kappa+1)\left(\frac{1}{2}|\nabla u_0|^2 +\frac{1}{2}|u_1|^2+\frac{1}{p+1}|u_0|^{p+1}\right) dx < +\infty.  \] If $p=3$, we can also prove the scattering result if initial data$(u_0,u_1)$ are contained in the critical Sobolev space and satisfy theinequality \[  \int_{{\mathbb R}^3} |x|\left(\frac{1}{2}|\nabla u_0|^2 +\frac{1}{2}|u_1|^2+\frac{1}{4}|u_0|^{p+1}\right) dx < +\infty. \] Theseassumptions on the decay rate of initial data as $|x| \rightarrow \infty$ areweaker than previously known scattering results.

Inward/outward Energy Theory of Non-radial Solutions to 3D Semi-linear Wave Equation