@article{ISI:000437962900008,
 abstract = {The Beale-Kato-Majda theorem contains a single criterion that controls
the behaviour of solutions of the 3D incompressible Euler equations.
Versions of this theorem are discussed in terms of the regularity issues
surrounding the 3D incompressible Euler and Navier-Stokes equations
together with a phase-field model for the statistical mechanics of
binary mixtures called the 3D Cahn-Hilliard-Navier-Stokes (CHNS)
equations. A theorem of BKM-type is established for the CHNS equations
for the full parameter range. Moreover, for this latter set, it is shown
that there exists a Reynolds number and a bound on the energy
dissipation rate that, remarkably, reproduces the Re-3/4 upper bound on
the inverse Kolmogorov length normally associated with the Navier-Stokes
equations alone. An alternative length-scale is introduced and
discussed, together with a set of pseudo-spectral computations on a
128(3) grid. (C) 2017 Elsevier B.V. All rights reserved.},
 author = {Gibbon, John D. and Gupta, Anupam and Pal, Nairita and Pandit, Rahul},
 doi = {10.1016/j.physd.2017.11.007},
 eissn = {1872-8022},
 issn = {0167-2789},
 journal = {PHYSICA D-NONLINEAR PHENOMENA},
 month = {AUG 1},
 number = {SI},
 orcid-numbers = {Gupta, Anupam/0000-0002-7335-0584},
 pages = {60-68},
 researcherid-numbers = {Gupta, Anupam/N-4777-2018},
 times-cited = {3},
 title = {The role of BKM-type theorems in 3D Euler, Navier-Stokes and
Cahn-Hilliard-Navier-Stokes analysis},
 unique-id = {ISI:000437962900008},
 volume = {376},
 year = {2018}
}