181 citations
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math.AP2008★ 1 cited
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.
math.AP2007
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…
math.AP2006★ 31 cited
Title Scattering of Solitons for Schrödinger Equation Coupled to a Particle
Alexander Komech, Elena Kopylova
We establish soliton-like asymptotics for finite energy solutions to the Schrödinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close…