Iitaka's $C_{n,m}$ conjecture for 3-folds in positive characteristic

In this paper, we prove that for a fibration $f:X\to Z$ from a smooth projective 3-fold to a smooth projective curve, over an algebraically closed field $k$ with $\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}k=p>5$, if the geometric generic fiber $X_{\bar{\eta }}$ is smooth, then subadditivity of Kodaira dimensions holds, i.e. $$\kappa (X)\ge \kappa (X_{\bar{\eta }})+\kappa (Z)\mathrm{.}$$