@article{ISI:000397422700011,
 abstract = {We consider the three-dimensional (3D) Cahn-Hilliard equations coupled
to, and driven by, the forced, incompressible 3D Navier-Stokes
equations. The combination, known as the Cahn-Hilliard-Navier-Stokes
(CHNS) equations, is used in statistical mechanics to model the motion
of a binary fluid. The potential development of singularities (blow-up)
in the contours of the order parameter phi is an open problem. To
address this we have proved a theorem that closely mimics the
Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J.
T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)].
By taking an L-infinity norm of the energy of the full binary system,
designated as E-infinity, we have shown that integral(1)(0)
E-infinity(tau)d tau governs the regularity of solutions of the full 3D
system. Our direct numerical simulations (DNSs) of the 3D CHNS equations
for (a) a gravity-driven Rayleigh Taylor instability and (b) a
constant-energy-injection forcing, with 128(3) to 512(3) collocation
points and over the duration of our DNSs confirm that E-infinity remains
bounded as far as our computations allow.},
 article-number = {063103},
 author = {Gibbon, John D. and Pal, Nairita and Gupta, Anupam and Pandit, Rahul},
 doi = {10.1103/PhysRevE.94.063103},
 eissn = {2470-0053},
 issn = {2470-0045},
 journal = {PHYSICAL REVIEW E},
 month = {DEC 12},
 number = {6},
 orcid-numbers = {Gupta, Anupam/0000-0002-7335-0584},
 researcherid-numbers = {Gupta, Anupam/N-4777-2018},
 times-cited = {4},
 title = {Regularity criterion for solutions of the three-dimensional
Cahn-Hilliard-Navier-Stokes equations and associated computations},
 unique-id = {ISI:000397422700011},
 volume = {94},
 year = {2016}
}