**Date: **October 9th at 5:00 pm, Aula Riunioni (Maths Department)

**Abstract:**

In this talk, a finite element approximation of the steady $p(\cdot)$-Navier–Stokes equations ($p(\cdot)$ is variable dependent) is examined for orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Numerical experiments confirm the quasi-optimality of the *a priori* error estimates (for the velocity).

The steady $p(\cdot)$-Navier–Stokes equations are a prototypical example of a non-linear system with variable growth conditions. They appear naturally in physical models for so-called *smart fluids*, *e.g.*, electro-rheological fluids, micro-polar electro-rheological fluids, magneto-rheological fluids, chemically reacting fluids, and thermo-rheological fluids, and have the potential for an application in numerous areas, *e.g.*, in electronic, automobile, heavy machinery, military, and biomedical industry.