On the stationary Oseen equations in \(\mathbb R^3\). (English) Zbl 1235.35216

Amrouche, Chérif; Consiglieri, Luisa

Commun. Math. Anal. 10, No. 1, 5-29 (2011).

Summary: The stationary Oseen equations are studied in \(\mathbb R^3\) in its general form, that is, with a non-constant divergenceless function on the convective term. We prove existence, uniqueness and regularity results in weighted Sobolev spaces. From this new approach, we also state existence, uniqueness and regularity results for the generalized Oseen model which describes the rotating flows. The proofs are based on Laplace, Stokes and Oseen theories.

MSC:

35Q35	PDEs in connection with fluid mechanics
76D07	Stokes and related (Oseen, etc.) flows

Keywords:

Stokes equations; Oseen equations; weighted Sobolev spaces