On the existence and regularity of solutions for degenerate power-law fluids

Abstract

The authors study time-dependent flows of incompressible degenerate $p$-power law fluids with periodic boundary conditions. They prove and utilize higher regularity of solutions to obtain a priori estimates for the velocity gradients in a suitable Nikol\cprime ski\u\i space.

Combining this with a standard Galerkin approximation, they prove the existence of solutions for $p}2$ in three dimensions.

Keywords

• existence
• regularity
• solutions
• degenerate
• power-law
• fluids