Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth  

作　　者：Lingwei Ma Zhenqiu Zhang 

机构地区：[1]School of Mathematical Sciences,Tianjin Normal University,Tianjin,300387,China [2]School of Mathematical Sciences and LPMC,Nankai University,Tianjin,300071,China

出　　处：《Science China Mathematics》2024年第7期1525-1554,共30页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 12101452 and 12071229)。

摘　　要：This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+■π=f,div u=0,where Du is the symmetric part of the gradient■u.We first establish anε-regularity criterion involving both the excess functional of the symmetric gradient Du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of Du in an open subset Ω_(u) of Ω with full measure.Such anε-regularity criterion leads to a pointwise Wolff potential estimate of Du,which immediately infers that Du is partially C^(0)-regular under appropriate assumptions.Finally,we give a local continuous modulus estimate of Du.

关 键 词：nonlinear Stokes system partial regularity Wolff potential estimates continuous modulus estimates 

分 类 号：O175[理学—数学]