Fundamental Serrin type regularity criteria for 3D MHD fluid passing through the porous medium

Zhang, Zujin; Zhong, Dingxing; Gao, Shujing; Qiu, Shulin

doi:10.2298/fil1705287z

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2019

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“…In 2017, Gu and Shen [10] got the asymptotic behaviors of the Green functions as well as the convergence rates in L p and L ∞ for solutions. Recently, other authors have also been interested in the regularity estimates for the Stokes problems, see [3,5,11,23] and their references for more results.…”

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confidence: 99%

Convergence rates of nonlinear Stokes problems in homogenization

Wang

Zhao

2019

Bound Value Probl

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In this paper, we study the convergence rates of solutions in homogenization of nonlinear Stokes Dirichlet problems. The main difficulty of this work is twofold. On the one hand, the nonlinear Stokes problems do not fit the standard framework of second-order elliptic equations in divergence form. On the other hand, nonlinear problems may cause new difficulties in the estimation of the quantity as well as first-order approximate term. As a consequence, we establish the sharp rates of convergence in H 1 and L 2. This work may be regarded as an extension of the approach for the linear Stokes problems to the nonlinear case.

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