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20052023
most citedSharp estimates for the number of degrees of freedom for the damped-driven 2D Navier--Stokes equations

47 citations · 85 across the 21 of their papers we have counts for

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Showing 2009Show all

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math.AP2009★ 1 cited

On the regularization mechanism for the periodic Korteweg-de Vries equation

Anatoli V. Babin, Alexei A. Ilyin, Edriss S. Titi

In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg--de Vries (KdV) equation in the homogeneous S…

math.AP2009

Lower bounds for the spectrum of the Laplace and Stokes operators

Alexei A. Ilyin

We prove Berezin--Li--Yau-type lower bounds with additional term for the eigenvalues of the Stokes operator and improve the previously known estimates for the Laplace operator. Gen…