— We present an existence resuit for the global attractor associated to the NavierStokes Equations in an infinité stnp in Ifê, and provide an estimate for Us fractal dimension in terms o f the Reynolds number

We establish the eventual regularity of suitably defined weak solutions to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. The existence of a global attractor of the Boussinesq system at large Prandtl number is also presented.

In this paper we study analytically the viscous ‘sabra’ shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a finite dimensional global attractor and globally invariant inertial manifolds. Moreover, we establish the existence of exponentially decaying energy dissipation ...

We consider the global attractor Af for the semiflow generated by a scalar semilinear parabolic equation of the form ut = uxx + f(u, ux), defined on the circle, x ∈ S. Using a characterization of the period maps for planar Hamiltonian systems of the form u′′ + g(u) = 0 we discuss questions related to the topological equivalence between global attractors.

We apply a semi-discrete in time relaxation scheme to a weakly damped forced nonlinear Schrödinger system. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a global attractor for this dynamical system.

We consider a generalized nonlocal Ginzburg–Landau equation with periodic boundary conditions. For the corresponding initial-boundary value problem we prove existence of solution for all positive values evolution variable. study and properties invariant manifolds. extract class manifolds union which forms global attractor. describe structure attractor find Euclidean dimension its components. In...

The 2D incompressible Boussinesq system with partial or fractional dissipation have recently attracted considerable attention. In this paper, we study the Cauchy problem for the 2D Boussinesq system in a periodic domain with fractional vertical dissipation in the subcritical case, and we prove the global well-posedness of strong solutions. Based on this, we also discuss the existence of the glo...