The Asymptotic Properties of Turbulent Solutions to the Navier-Stokes Equations

Zdenek Skalák


In this paper we study the large time behavior of solutions to the Navier-Stokes equations. We present a brief survey of results concerning energy decay, and discuss a related phenomenon of the large time energy concentration in the frequency space occurring in any turbulent solution. This leads us to the study of solutions in the Besov spaces and to proof that if we choose a suitable initial condition then in some Besov spaces the energy of the associated solution does not decrease asymptotically to zero.


Navier-Stokes equations; Besov spaces

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague