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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…
On the spectrum of the Stokes operator
Alexei A. Ilyin
We prove Li--Yau-type lower bounds for the eigenvalues of the Stokes operator and give applications to the attractors of the Navier--Stokes equations.
On the Domain of Analyticity and Small Scales for the Solutions of the Damped-driven 2D Navier-Stokes Equations
Alexei A. Ilyin, Edriss S. Titi
We obtain a logarithmically sharp estimate for the space-analyticity radius of the solutions of the damped-driven 2D Navier-Stokes equations with periodic boundary conditions and r…
Sharp estimates for the number of degrees of freedom for the damped-driven 2D Navier--Stokes equations
Alexei A. Ilyin, Edriss S. Titi
We derive upper bounds for the number of asymptotic degrees (determining modes and nodes) of freedom for the two-dimensional Navier--Stokes system and Navier-Stokes system with dam…