On the Log Abundance for Compact {K{ä}hler} threefolds II

In this article we show that if $(X,\mathrm{\Delta })$ is a log canonical compact Kähler threefold pair such that $K_X+\mathrm{\Delta }$ is nef and the numerical dimension $\nu (X,K_X+\mathrm{\Delta })=2$, then $K_X+\mathrm{\Delta }$ is semi-ample. This result combined with our previous work in arXiv:2201.01202 shows that the log abundance holds for log canonical compact Kähler threefold pairs.