Higher Order Fractional Differentiability for the Stationary Stokes System

作     者：Ling Wei MA Zhen Qiu ZHANG Qi XIONG Ling Wei MA;Zhen Qiu ZHANG;Qi XIONG

作者机构：School of Mathematical SciencesTianjin Normal UniversityTianjin 300387P.R.China School of Mathematical Sciences and LPMCNankai UniversityTianjin 300071P.R.China School of Mathematical SciencesNankai UniversityTianjin 300071P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第1期

页      面：13-29页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：Higher order fractional differentiability Stokes system Besov spaces 

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,***)^(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).