ON REGULARITY OF THE TIME DERIVATIVE FOR DEGENERATE PARABOLIC SYSTEMS

Abstrakt

We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non-Newtonian fluids of powerlaw or Carreau type.

By the use of special weak different quotients adapted to the variational structure we bound fractional derivatives of ut in time and space directions. Although the estimates presented here are valid under very general assumptions they are a novelty even for the parabolic p-Laplace equation.

Klíčová slova

• degenerate parabolic systems
• regularity of PDE
• non-Newtonian fluids