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Compacité par compensation et espaces de Hardy. (Compactness by compensation and Hardy spaces.). (French) Zbl 0705.46015

Sémin. Équations Dériv. Partielles 1989-1990, No. 14, 8 p. (1990).
For the nonlinear expressions det(\(\nabla u)\), \(\sum \frac{\partial u_ i}{\partial x_ j}\frac{\partial u_ j}{\partial x_ i}\) and \(\sum u_ iv_ i\), better regularity properties are obtained. They consist in substituting a generalized Hardy space for \(L^ 1\). Applications (e.g. Navier-Stokes equations) and extensions are discussed.
Reviewer: C.Marinov

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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