Differential and Integral Equations

Sharp Sobolev interpolation inequalities for the Stokes operator

Wenzheng Xie

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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


Export citation