Global well-posedness for second grade fluids

Abstract

This paper deals with a study on an initial-boundary value problem for incompressible non-Newtonian fluids of degree two, in a bounded and simply connected open set [Formula: see text] of [Formula: see text]. It will be shown that the global-in-time weak solution is uniformly stable (i.e. the behavior of the solution changes continuously with the data), and consequently this solution is unique. Furthermore, an exponential decay rate for the energy of the weak solution will also be established.