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Concentration-cancellation and Hardy spaces

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  09 April 2009

Italo Vecchi
Italo Vecchi
Affiliation:
Seminar für Angewandte Mathematik, ETH-Zentrum, CH-8092, Zürich, Switzerland
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Abstract

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Let υ∈ be a sequence of DiPema-Majda approximate solutions to the 2-d incompressible Euler equations. We prove that if the vorticity sequence is weakly compact in the Hardy space H1 (R2) then a subsequence of υ∈ converges strongly in the energy norm to a solution of the Euler equations.

MSC classification

Secondary: 76D05: Navier-Stokes equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 1 , February 1995 , pp. 94 - 99
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Adams, R., Sobolev spaces (Academic Press, New York, 1975).Google Scholar
[2]Coifman, R. R. and Weiss, G., ‘Extensions of Hardy spaces’, Bull. Amer. Math. Soc. (N.S.) 83 (1977), 569–645.CrossRefGoogle Scholar
[3]Delort, J., ‘Existence de nappes de tourbillon en dimension deux’, J. Amer. Math. Soc. 4 (1991), 553–586.CrossRefGoogle Scholar
[4]DiPerna, R. J. and Majda, A., ‘Concentrations in regularizations for 2-D incompressible flow’, Comm. Pure Appl. Math. 40 (1987), 302–345.CrossRefGoogle Scholar
[5]Dipema, R. J. and Majda, A., ‘Oscillations and concentrations in weak solutions of the incompressible fluid equations’, Comm. Math. Phys. 108 (1987), 667–689.Google Scholar
[6]Dipema, R. J. and Majda, A., ‘Reduced Hausdorff dimension and concentration cancellation for 2-D incompressible flow’, J. Amer. Math. Soc. 1 (1988), 59–95.Google Scholar
[7]Ekeland, I. and Temam, R., Convex analysis and variational problems (North Holland, Amsterdam, 1982).Google Scholar
[8]Torchinsky, A., Real variable methods in harmonic analysis (Academic Press, New York, 1986).Google Scholar