A note on Iitaka's conjecture $C_{3,1}$ in positive characteristics

Let $f:X\to Y$ be a fibration from a smooth projective 3-fold to a smooth projective curve, over an algebraically closed field $k$ of characteristic $p

5$\mathrm{.}Weprovethatifthegenericfiber$X_{\eta}$hasbigcanonicaldivisor$K_{X_{\eta}}$,then$$\kappa (X)\ge \kappa (Y)+\kappa (X_{\eta })\mathrm{.}$$