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On the time analyticity radius of the solutions of the two-dimensional Navier-Stokes equations. (English) Zbl 0744.35033

The paper deals with the Navier-Stokes equations in \(\Omega=[0,1]\times[0,1]\) with periodic boundary conditions. The following analyticity property is established. If the initial datum lies on the global attractor and is close enough to a stationary solution, then the analyticity radius at \(t=0\) of the solution can be made arbitrarily large.

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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References:

[1] Constantin, P., and Foias, C. (1988).Navier-Stokes Equations, Chicago Lectures in Mathematics, Chicago/London. · Zbl 0687.35071
[2] Foias, C., and Temam, R. (1979). Some analytic and geometric properties of the solutions of the Navier-Stokes equations.J. Math. Pures Appl. 58, 339-368. · Zbl 0454.35073
[3] Ladyzhenskaya, O. A. (1972). On the dynamical system generated by the Navier-Stokes equations.Zap. Nauch. Sem. LOMI 27, 91-114. [English translation,J. Soviet Math. 28, 458-479 (1975).] · Zbl 0301.35077
[4] Temam, R. (1988).Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci. No. 68, Springer, New York. · Zbl 0662.35001
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