Differential and Integral Equations

On Oseen resolvent estimates

Paul Deuring and Werner Varnhorn

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Abstract

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

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

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019077

Mathematical Reviews number (MathSciNet)
MR2742482

Zentralblatt MATH identifier
1240.35381

Subjects
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]

Citation

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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