Abstract
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 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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Acknowledgements
The authors are very grateful to Professor G. Mingione for suggesting this interesting problem to us. The authors are supported by the National Natural Science Foundation of China (NNSF Grant No. 12101452 , No. 12071229 and No. 12001333), and Shandong Provincial Natural Science Foundation (Grant No. ZR2020QA005).
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Ma, L., Zhang, Z. & Zhou, F. Nonlinear Potential Estimates for Generalized Stokes System. Mediterr. J. Math. 19, 212 (2022). https://doi.org/10.1007/s00009-022-02135-x
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DOI: https://doi.org/10.1007/s00009-022-02135-x