The Lamm-Rivi\`ere system II: energy identity

In this paper, we establish an angular energy quantization for the following fourth order inhomogeneous Lamm-Rivi\`ere system $$\Delta^2u=\Delta(V\cdot\nabla u)+\text{div}(w\nabla u)+W\cdot\nabla u+f$$ in dimension four, with an inhomogeneous term $f\in L\log L$.