We prove the existence of inertial manifolds for the incompressible hyperviscous Navier–
Stokes equations on the two or three-dimensional torus:{u t+ ν (− Δ) β u+(u⋅∇) u+∇ p= f,(t …

We investigate the long-term behavior, as a certain regularization parameter vanishes, of the
three-dimensional Navier–Stokes–Voigt model of a viscoelastic incompressible fluid. We …

The paper gives a comprehensive study of inertial manifolds for semilinear parabolic
equations and their smoothness using the spatial averaging method suggested by Sell and …

The dependence of the fractal dimension of global attractors for the damped 3D Euler–
Bardina equations on the regularization parameter α> 0 and Ekman damping coefficient γ> …

The Tokamak device is the most promising candidate for producing sustainable electric
power by nuclear fusion. It is a torus-shaped device that confines plasma by a strong …

This paper deals with the asymptotic compactness of the solutions of the two-dimensional
Navier-Stokes equations defined in unbounded channel-like domains. In order to overcome …

We discuss the estimates for the $ L^ p $-norms of systems of functions that are orthonormal
in $ L^ 2$ and $ H^ 1$, respectively, and their essential role in deriving good or even …

We consider a general family of regularized models for incompressible two-phase flows
based on the Allen–Cahn formulation in n n-dimensional compact Riemannian manifolds for …

This paper investigates the existence and upper semi-continuity of the pullback measure
attractors of the non-autonomous stochastic 3D globally modified Navier–Stokes equations …

This paper aims to study a family of Leray-α models with periodic boundary conditions.
These models are good approximations for the Navier–Stokes equations. We focus our …