Differential and Integral Equations

Sharp Sobolev interpolation inequalities for the Stokes operator

Wenzheng Xie

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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

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

First available in Project Euclid: 2 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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