Let $S=\mathrm{Spec}(R)$, $s=\mathrm{Spec}(k)$ and $\eta=\mathrm{Spec}(K)$, where $R$ is a d.v.r. with fraction field $K$. Let $j:\eta\rightarrow S$

Now how to compute the sheaf $R^1j_*(\mathbb{G}_{m,\eta})$ in the fppf topology?

The case for etale topology is zero by considering the stalks and use the Hilbert 90.