Approximate controllability of second grade fluids

TL;DR

This paper proves that second grade non-Newtonian fluids on a 2D torus can be approximately controlled using finite-dimensional control forces, extending controllability results to complex fluid models.

Contribution

It demonstrates approximate controllability of second grade fluids with finite-dimensional controls, applying and extending existing control methods to this non-Newtonian fluid class.

Findings

Second grade fluids are approximately controllable on a 2D torus.

Finite-dimensional control forces suffice for controllability.

The methods of Agrachev-Sarychev and Sirikyan are effectively applied.

Abstract

This paper deals with the controllability of the second grade fluids, a class of non-Newtonian of differentiel type, on a two-dimensional torus. Using the method of Agrachev-Sarychev [1], [2] and of Sirikyan [26], we prove that the system of second grade fluids is approximately controllable by a finite-dimensional control force.