## Differential and Integral Equations

### Sharp Sobolev interpolation inequalities for the Stokes operator

Wenzheng Xie

#### 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