Locally nilpotent derivations on ${\mathbb{A}}^2$-fibrations with ${\mathbb{A}}^1$-fibration kernels

In this paper, we give a characterization of locally nilpotent derivations on ${\mathbb{A}}^2$-fibrations over Noetherian domains containing $\mathbb{Q}$ having kernel isomorphic to an ${\mathbb{A}}^1$-fibration.