Let $k$ be a field of characteristic zero and $A$ be a $k$-algebra. A derivation on $A$ is a $k$-linear map $D: A \to A$ such that $D(ab)=aD(b)+bD(a), \forall a,b \in A$. A derivation is called locally nilpotent if for every $a\in A$, $\exists n_a\in \mathbb N$ such that $D^{n_a} (a)=0$, where $D^n$ means $D$ composed with itself $n$-times.

My question is : Given a finitely generated $k$-algebra $A$ which is also an integral domain, does there exist a locally nilpotent derivation on $A[X,Y]$ whose kernel is $A$ ?