Asymptotic energy and enstrophy concentration in solutions to the Navier-Stokes equations in R3

被引:0
作者
Skalák Z. [1 ]
机构
[1] Institute of Hydrodynamics, 166 12 Prague 6
关键词
Asymptotic behavior; Energy concentration; Enstrophy concentration; Fast decays; Navier-Stokes equations;
D O I
10.1007/s11565-009-0073-5
中图分类号
学科分类号
摘要
Let A be the Stokes operator. We show as the main result of the paper that if w is a nonzero global weak solution to the Navier-Stokes equations in R3 satisfying the strong energy inequality, then the energy of the solution w concentrates asymptotically in frequencies smaller than or equal to the finite number (Formula presented.) in the sense that (Formula presented.) for every λ > C(1/2), where {Eλ; λ ≥ 0} is the resolution of identity of A. We also obtain an explicit convergence rate in the limit above and similar results for the enstrophy of w defined as {double pipe}A1/2w{double pipe}. © Università degli Studi di Ferrara 2009.
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页码:377 / 394
页数:17
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