In this paper, we discuss syzygies and quotient equations of the two-dimensional Euler system of PDEs. We use some of the previously obtained results concerning kinematic symmetries and invariants of the system to find the quotient. It follows from the theorem describing the field of differential invariants that there are ten relations (syzygies) between the second-order invariants. Choosing zero- and first-order invariants as Lie–Tresse coordinates and expressing Tresse derivatives, we obtain the quotient.
Duyunova et al. (Sat,) studied this question.