LAUSR

Abstract We consider the Oseen system with resolvent term in an exterior domain in R 3 , supplemented by homogeneous Dirichlet boundary conditions. Under the assumption that the resolvent parameter λ is close to zero and ℜ λ ≥ 0 , λ ≠ 0 , we estimate the L p -norm of the velocity against the L p -norm of the right-hand side, times a factor C | λ | − 2 , with C > 0 independent of λ. Such an estimate cannot hold for this range of λ if | λ | − 2 is replaced by | λ | − κ with κ 3 / 2 , and there are indications that κ ∈ [ 3 / 2 , 2 ) cannot be admitted either. We present various other L p -estimates of Oseen resolvent flows for the same range of λ. Our article is complementary to the work by T. Kobayashi and Y. Shibata (1998) [20] , where Oseen resolvent estimates are derived under the assumption that | λ | ≥ c 0 , for some arbitrary but fixed c 0 > 0 , with the constant in the resolvent estimate depending on c 0 .