Campanato estimates for the generalized Stokes System
Lars Diening, Petr Kaplicky, Sebastian Schwarzacher
TL;DR
This paper establishes optimal regularity estimates in BMO and Campanato spaces for solutions to a generalized stationary Stokes system, extending to Navier-Stokes and evolutionary variants.
Contribution
It provides new optimal regularity results for a broad class of generalized Stokes systems with nonlinear elliptic operators.
Findings
Optimal BMO estimates for A(Du)
Optimal Campanato estimates for A(Du)
Implications for generalized Navier-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 div(A(Du)), where D is the symmetric part of the gradient. The model case is A(Du)=(kappa+|Du|)^{p-2}Du. We show optimal BMO and Campanato estimates for A(Du). Some corollaries for the generalized stationary Navier-Stokes system and for its evolutionary variant are also mentioned.
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