Dynamics of Partial Differential Equations

Volume 4 (2007)

Number 2

On the domain of analyticity and small scales for the solutions of the damped-driven 2d Navier–Stokes equations

Pages: 111 – 127

DOI: https://dx.doi.org/10.4310/DPDE.2007.v4.n2.a1

Authors

Alexei A. Ilyin (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia)

Edriss S. Titi (Department of Mathematics, University of California at Irvine)

Abstract

We obtain a logarithmicaly sharp estimate for the space-analyticity radius of the solutions of the damped-driven 2D Navier–Stokes equations with periodic boundary conditions and relate this to the small scales in this system. This system is inspired by the Stommel–Charney barotropic ocean circulation model.

Keywords

analyticity, Gevrey regularity, Navier–Stokes equations, dissipative length scales, Stommel–Charney model

2010 Mathematics Subject Classification

35B41, 35Q30, 37L30

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Published 1 January 2007