Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids

Abstract

We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times.

The example we have in mind foremost are materials with memory.

Keywords

• Incompressible fluid
• Viscosity depending on concentration
• Unsteady flows
• Nonlocal equation