The aim of this work is twofold: proving the existence of solution (u, π) ∈ H 1 (Ω)×L 2 (Ω) in bounded domains of R 2 and the whole plane for the Oseen problem (O) for solenoidal vector fields v in L 2 (Ω), and analyzing the same problem in bounded domains of R n for n = 2, 3 when h = 0, g = 0 and the solenoidal field v belongs to L s (Ω) for s < n.