Differential and Integral Equations

On Oseen resolvent estimates

Paul Deuring and Werner Varnhorn

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We consider the resolvent problem for the Oseen system and for the scalar Oseen equation in the whole space $\mathbb{R}^{3}$. It is shown that, for small values of the resolvent parameter, it is impossible to obtain an L$^{2}$-estimate analogous to the one that is valid for the Stokes resolvent, even if the resolvent parameter has positive real part.

Article information

Differential Integral Equations, Volume 23, Number 11/12 (2010), 1139-1149.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76D05: Navier-Stokes equations [See also 35Q30]


Deuring, Paul; Varnhorn, Werner. On Oseen resolvent estimates. Differential Integral Equations 23 (2010), no. 11/12, 1139--1149. https://projecteuclid.org/euclid.die/1356019077

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