Steady Stokes equations

Abstract

The first section of this chapter is dedicated to the proof of the Necas inequality which says that, in the space L 2(Ω), the L 2-norm is equivalent to the sum of the H -1-norm of the function and of its gradient. Even if this seems to be a very natural property, the proof (given here in any Lipschitz domain with compact boundary) is far from being straightforward.