Existence Theory for Generalized Newtonian Fluids

Preface

In continuum mechanics, the motion of an incompressible, homogeneous fluid is described by the velocity field and the hydrodynamical pressure. The time evolution of the fluid is governed by the Navier–Stokes system of partial differential equations which describes the balance of mass and momentum. In the classical formulation – which goes back to C.-L. Navier and G.G. Stokes – the relation between the viscous stress tensor and the symmetric gradient of the velocity field is linear (i.e. we have a Newtonian fluid). This system is already quite challenging from a mathematical point of view and has fascinated many mathematicians. However, it can only model fluids with a very simple molecular structure such as water, air and several ...