Incompressible fluids with shear rate and pressure dependent viscosity: regularity of steady planar flows

Abstract

In the article the regularity of steady planar flow of fluids where the shearing stress may depend on the symmetric part of the velocity vector field and the pressure is studied. The periodic boundary conditions are considered.

Using Meyers estimates it is shown that there exists a solution which is smooth. In the case where it is allowed to test weak formulation of the problem with a weak solution regularity of all weak solutions is proved.

Keywords

• Incompressible
• fluids
• shear
• pressure
• dependent
• viscosity
• regularity
• steady
• planar
• flows