Soliton resolution for the energy critical wave equation with inverse-square potential in the radial case

Abstract

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 $N\ge 3$. The structure of the radial linear operator ${\mathcal{L}}_a:=-\Delta +\frac{a}{|x{|}^2}=A^{\ast }A$, is essential for the channel of energy, where $A$ is a first order differential operator and $A^{\ast }$ is its adjoint operator. Modulation and analysis of the multi-solitons are performed in the function spaces ${\dot{H}}_a^1({\mathbb{R}}^N)\times L^2({\mathbb{R}}^N)$ associated with ${\mathcal{L}}_a$.

69 pages