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A variational approach to the Navier–Stokes equations

Authors
Journal
Bulletin des Sciences Mathématiques
0007-4497
Publisher
Elsevier
Volume
136
Issue
3
Identifiers
DOI: 10.1016/j.bulsci.2012.01.001

Abstract

Abstract We propose a time discretization of the Navier–Stokes equations inspired by the theory of gradient flows. This discretization produces Leray/Hopf solutions in any dimension and suitable solutions in dimension 3. We also show that in dimension 3 and for initial datum in H1, the scheme converges to strong solutions in some interval [0,T) and, if the datum satisfies the classical smallness condition, it produces the smooth solution in [0,∞).

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