This book develops the theory of global attractors for a class of parabolic PDEs that includes
reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated …

We consider reaction-diffusion systems in unbounded domains, prove the existence of
expotential attractors for such systems, and estimate their fractal dimension. The essential …

Introduction. The answer to the question above is: Until the early eighties, very little; since
then, quite a lot. In fact, the Navier–Stokes equations now provide a corroborating testimony …

Lattice Boltzmann methods provide a robust and highly scalable numerical technique in
modern computational fluid dynamics. Besides the discretization procedure, the relaxation …

Abstract We study the Navier-Stokes equation forced by white in time stochastic noise
constructed as the weighted, infinite sum of standard Brownian motions. Using martingale …

We consider the solutions lying on the global attractor of the two-dimensional Navier–Stokes
equations with periodic boundary conditions and analytic forcing. We show that in this case …

In this paper we present a new construction of exponential attractors based on the control of
Lyapunov exponents over a compact, invariant set. The fractal dimension estimate of the …

CLAUDE BARDOS and BASILE NICOLAENKO Navier Stokes Equations { and Dynamical
Systems CONTENTS 1. Introduction. 2. Euler and Navie Page 1 CLAUDE BARDOS and BASILE …

We consider the numerical solution of nonlinear, dissipative partial differential equations
using a pseudospectral method and the methodology of approximate inertial manifolds …