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Pré-Publication, Document De Travail Année : 2010

Sums of large global solutions to the incompressible Navier-Stokes equations

Résumé

Let G be the (open) set of~$\dot H^{\frac 1 2}$ divergence free vector fields generating a global smooth solution to the three dimensional incompressible Navier-Stokes equations. We prove that any element of G can be perturbed by an arbitrarily large, smooth divergence free vector field which varies slowly in one direction, and the resulting vector field (which remains arbitrarily large) is an element of G if the variation is slow enough. This result implies that through any point in G passes an uncountable number of arbitrarily long segments included in G.
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Dates et versions

hal-00459759 , version 1 (25-02-2010)
hal-00459759 , version 2 (01-10-2010)

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Jean-Yves Chemin, Isabelle Gallagher, Ping Zhang. Sums of large global solutions to the incompressible Navier-Stokes equations. 2010. ⟨hal-00459759v2⟩
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