Differential and Integral Equations

Sharp Sobolev interpolation inequalities for the Stokes operator

Wenzheng Xie

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Abstract

We prove Sobolev interpolation inequalities for the Stokes operator, giving sharp $L^{\infty}$ estimates for solenoidal vector fields in $\mathbb{R}^2$ and $\mathbb{R}^3$. We use fundamental solutions of a generalized Stokes system in the proofs.

Article information

Source
Differential Integral Equations, Volume 10, Number 2 (1997), 393-399.

Dates
First available in Project Euclid: 2 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367526345

Mathematical Reviews number (MathSciNet)
MR1424819

Zentralblatt MATH identifier
0892.46030

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 76D07: Stokes and related (Oseen, etc.) flows

Citation

Xie, Wenzheng. Sharp Sobolev interpolation inequalities for the Stokes operator. Differential Integral Equations 10 (1997), no. 2, 393--399. https://projecteuclid.org/euclid.die/1367526345


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