Energy identity for the maps from a surface with tension field bounded in $L^p$

Let $M$ be a closed Riemannian surface and $u_n$ a sequence of maps from $M$ to Riemannian manifold $N$ satisfying $$\underset{n}{\sup }(\mathrm{\parallel }\mathrm{\nabla }{u}_n{\mathrm{\parallel }}_{L^2(M)}+\mathrm{\parallel }\tau (u_n){\mathrm{\parallel }}_{L^p(M)})\le \mathrm{\Lambda }$$ for some $p>1$, where $\tau (u_n)$ is the tension field of the mapping $u_n$. For the general target manifold $N$, if $p\ge \frac{6}{5}$, we prove the energy identity and neckless during blowing up.