Non-Newtonian fluids with discontinuous-in-time stress tensor

Abstract

We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically (s - 1)-growth with the parameter s depending on the spatial and time variable.

We do not assume any smoothness of s with respect to time variable and assume the log-Holder continuity with respect to spatial variable. Such a setting is a natural choice if the material properties are instantaneous, e.g. changed by the switched electric field.

We establish the long time and the large data existence of weak solution.

Keywords

• Incompressible flow
• Non-Newtonian fluid
• Non-standard growth
• Generalized Lebesgue space
• Musielak-Orlicz space