Nonlinear Potential Estimates for Generalized Stokes System

Lingwei Ma; Zhenqiu Zhang; Feng Zhou

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arXiv · 2108.03796

Nonlinear Potential Estimates for Generalized Stokes System

Lingwei Ma·Zhenqiu Zhang·Feng Zhou

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Abstract

In this paper, we consider the generalized stationary Stokes system with $p$-growth and Dini-$\operatorname{BMO}$ 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 $L^{\infty}$ 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.

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Lingwei Ma, Zhenqiu Zhang, Feng Zhou. 2021-08-09. Nonlinear Potential Estimates for Generalized Stokes System. https://arxiv.org/abs/2108.03796

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