On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model

Abstract

We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term E >Delta(3). We establish the global existence, uniqueness, and regularity of solutions.

Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of E > > 0.

Keywords

• Ladyzhenskaya fluid
• Exponential attractor
• Fractal dimension
• Lyapunov exponents