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Published in:
2013 | OriginalPaper | Chapter
Steady Stokes equations
Authors : Franck Boyer, Pierre Fabrie
Published in: Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models
Publisher: Springer New York
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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.