Nonlinear Potential Estimates for Generalized Stokes System

In this paper, we consider the generalized stationary Stokes system with p -growth and Dini- $${\text {BMO}}$$ regular coefficients. The main purpose is to establish pointwise estimates for shear rate associated pressure such in terms of an unconventional nonlinear Havin–Maz’ya–Wolff type potential nonhomogeneous term plane. As a consequence, symmetric gradient $$L^{\infty }$$ estimate obtained. Moreover, derive weak solution without additional regularity assumptions on coefficients higher dimensional space.