Nonlinear Potential Estimates for Generalized Stokes System

In this paper, we consider the generalized stationary Stokes system with p -growth and DiniBMO regular coefficients. The main purpose is to establish pointwise estimates for the shear rate and the associated pressure to such Stokes system in terms of an unconventional nonlinear Havin-Maz’ya-Wolff type potential of the nonhomogeneous term in the plane. As a consequence, a symmetric gradient L∞ estimate is obtained. Moreover, we derive potential estimates for the weak solution to the Stokes system without additional regularity assumptions on the coefficients in higher dimensional space. Mathematics Subject classification (2020): 35Q35; 35J92; 35B65.

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