Higher Order Fractional Differentiability for the Stationary Stokes System  

作　　者：Ling Wei MA Zhen Qiu ZHANG Qi XIONG 

机构地区：[1]School of Mathematical Sciences,Tianjin Normal University,Tianjin 300387,P.R.China [2]School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,P.R.China [3]School of Mathematical Sciences,Nankai University,Tianjin 300071,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第1期13-29,共17页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.12071229,12101452);Tianjin Normal University Doctoral Research Project(Grant No.52XB2110)。

摘　　要：This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system{div A(x-Du)-■π=divF,inΩdivu=0,inΩ.In terms of the difference quotient method,our first result reveals that if F∈B_(p,q.loc)^(β)(Ω,R^(n))for p=2 and 1≤q≤2n/n-2β,then such extra Besov regularity can transfer to the symmetric gradient Du and its pressureπwith no losses under a suitable fractional differentiability assumption on x■A(x,ξ).Furthermore,when the vector field A(x,Du)is simplified to the full gradient■u,we improve the aforementioned Besov regularity for all integrability exponents p and q by establishing a new Campanato-type decay estimates for(■u,π).

关 键 词：Higher order fractional differentiability Stokes system Besov spaces 

分 类 号：O175[理学—数学]