In this paper, we establish the soliton resolution for the energy critical wave equation with inverse square potential in the radial case and in all dimensions $N\geq3$. The structure of the radial linear operator $\mathcal{ L}_a :=-\Delta +\frac{ a}{ |x|^2}=A^*A$, is essential for the channel of energy, where $A$ is a first order differential operator and $A^*$ is its adjoint operator. Modulation and analysis of the multi-solitons are performed in the function spaces $\dot{ H}^1_a(\Bbb R^N)\times L^2(\Bbb R^N)$ associated with $\mathcal{ L}_a$.
Categories: math.AP