Interior $L_{p}$ regularity for Stokes systems

Abstract

A new iteration method is represented to study the interior $L_{p}$ regularity for Stokes systems both in divergence form and in non-divergence form. By the iteration, we improve the integrability of derivatives of solutions for Stokes systems step by step; after infinitely many steps, $L_{p}$ regularity is achieved; and in each step, the maximal function method is used where solutions and their derivatives are involved simultaneously in each scale. The H\"{o}lder continuity of the coefficients in spatial variables is assumed to compensate the different scalings between the solutions and their derivatives.