In this paper, within the constructive algebraic analysis approach to linear systems, we study classical linear systems of partial differential (PD) equations in two or three independent variables with constant coefficients appearing in mathematical physics and engineering sciences such as the Stokes and Oseen equations studied in hydrodynamics. We first provide a precise algebraic description of the endomorphism ring of the left D-module associated with a linear PD system. Then, we use it to prove that the endomorphism ring of the Stokes and Oseen equations in R2 is a cyclic D-module, which allows us to conclude about the decomposition and factorization properties of these linear PD systems.