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@article{Gibbon:2019:10.1007/s00332-018-9484-8,
author = {Gibbon, JD},
doi = {10.1007/s00332-018-9484-8},
journal = {Journal of Nonlinear Science},
pages = {215--218},
title = {Weak and strong solutions of the 3D Navier–Stokes equations and their relation to a chessboard of convergent inverse length scales},
url = {http://dx.doi.org/10.1007/s00332-018-9484-8},
volume = {29},
year = {2019}
}

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TY  - JOUR
AB  - Using the scale invariance of the Navier–Stokes equations to define appropriate space-and-time-averaged inverse length scales associated with weak solutions of the 3D Navier–Stokes equations, on a periodic domain =[0,L]3 an infinite ‘chessboard’ of estimates for these inverse length scales is displayed in terms of labels (n,m) corresponding to n derivatives of the velocity field in L2m(). The (1,1) position corresponds to the inverse Kolmogorov length Re3/4. These estimates ultimately converge to a finite limit, Re3, as n,m→∞, although this limit is too large to lie within the physical validity of the equations for realistically large Reynolds numbers. Moreover, all the known time-averaged estimates for weak solutions can be rolled into one single estimate, labelled by (n,m). In contrast, those required for strong solutions to exist can be written in another single estimate, also labelled by (n,m), the only difference being a factor of 2 in the exponent. This appears to be a generalization of the Prodi–Serrin conditions for n≥1.
AU  - Gibbon,JD
DO  - 10.1007/s00332-018-9484-8
EP  - 218
PY  - 2019///
SN  - 0938-8974
SP  - 215
TI  - Weak and strong solutions of the 3D Navier–Stokes equations and their relation to a chessboard of convergent inverse length scales
T2  - Journal of Nonlinear Science
UR  - http://dx.doi.org/10.1007/s00332-018-9484-8
UR  - http://hdl.handle.net/10044/1/62041
VL  - 29
ER  -

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