Oseen resolvent estimates with small resolvent parameter

We consider the Oseen system with resolvent term in an exterior domain in R3, supplemented by homogeneous Dirichlet boundary conditions. Under the assumption that the resolvent parameter λ is close to zero and ℜλ≥0, λ≠0, we estimate the Lp-norm of the velocity against the Lp-norm of the right-hand s...

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Bibliographic Details
Published in:Journal of Differential Equations 2018-07, Vol.265 (1), p.280-311
Main Author: Deuring, Paul
Format: Article
Language:English
Subjects:
Incompressible Navier–Stokes system
Oseen term
Resolvent estimate
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Summary:We consider the Oseen system with resolvent term in an exterior domain in R3, supplemented by homogeneous Dirichlet boundary conditions. Under the assumption that the resolvent parameter λ is close to zero and ℜλ≥0, λ≠0, we estimate the Lp-norm of the velocity against the Lp-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 κ0, with the constant in the resolvent estimate depending on c0.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2018.02.033