Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations

On global attractors of the 3D Navier-Stokes equations

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 behavior of multi-valued dissipative evolutionary systems with respect to two topologies—weak and strong. Each such system possesses a global attractor in the weak topology, but not necessarily in the strong. In case the lat...

Global attractors for 3-dimensional stochastic Navier-Stokes equations

Sell’s approach [32] to the construction of attractors for the Navier– Stokes equations in 3-dimensions is extended to the 3-D stochastic equations with a general multiplicative noise.

Attractors and neo-attractors for 3D stochastic Navier-Stokes equations

In [14] nonstandard analysis was used to construct a (standard) global attractor for the 3D stochastic Navier–Stokes equations with general multiplicative noise, living on a Loeb space, using Sell’s approach [26]. The attractor had somewhat ad hoc attracting and compactness properties. We strengthen this result by showing that the attractor has stronger properties making it a neo-attractor – a ...

Measure Attractors for Stochastic Navier–stokes Equations

We show existence of measure attractors for 2-D stochastic Navier-Stokes equations with general multiplicative noise.

Attractors and Finite - Dimensional Behaviour in the Navier - Stokes Equations