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math.AP2012★ 2 cited
Navier-Stokes equations, determining forms, determining modes, inertial manifolds, dissipative dynamical systems
Ciprian Foias, Michael S. Jolly, Rostyslav Kravchenko +1
The determining modes for the two-dimensional incompressible Navier-Stokes equations (NSE) are shown to satisfy an ordinary differential equation of the form , in the B…
math.AP2006
On global attractors of the 3D Navier-Stokes equations
Alexey Cheskidov, Ciprian Foias
In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavio…