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Kolmogorov's Theory of Turbulence and Inviscid Limit of the Navier-Stokes Equations in ℝ 3

Abstract:

We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in ℝ 3. We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the α th-order fractional derivatives of the velocity for some α > 0 in the space variables in L 2, which is independent of the viscosity μ > 0. Then it is shown that this key observation yields the L 2-equicontinuity in the time variable and the uniform bound in L q, for some q > 2, of the vel...

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Publisher copy:
10.1007/s00220-011-1404-9
Journal:
Communications in Mathematical Physics More from this journal
Volume:
310
Issue:
1
Pages:
267-283
Publication date:
2012-02-01
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
Language:
English
Pubs id:
pubs:313940
UUID:
uuid:248fb22b-4991-48f4-8db0-f648d28f5fa1
Local pid:
pubs:313940
Source identifiers:
313940
Deposit date:
2013-11-16

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