Campanato estimates for the generalized Stokes System

Abstract

We study interior regularity of solutions of a generalized stationary Stokes problem in the plane. The main, elliptic part of the problem is given in the form , where is the symmetric part of the gradient.

The model case is. We show optimal and Campanato estimates for.

Some corollaries for the generalized stationary Navier-Stokes system and for its evolutionary variant are also mentioned.

Keywords

• Power law fluids
• Non-Newtonian
• Nonlinear Calderon-Zygmund theory
• Bounded mean oscillation
• Campanato estimates