Mixed-norm Lp-estimates for non-stationary Stokes systems with singular VMO coefficients and applications

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:276

Article

Dong, Hongjie¹  Tuoc Phan² 

[1] Brown Univ, Div Appl Math, 182 George St, Providence, RI 02912 USA

[2] Univ Tennessee, Dept Math, 227 Ayres Hall,1403 Circle Dr, Knoxville, TN 37996 USA

关键词: Time-dependent Stokes system;    Mixed-norm regularity estimates;    Navier-Stokes equations;    Leray-Hopf weak solutions;    Regularity criteria;   

DOI  :  10.1016/j.jde.2020.12.023

来源: Elsevier

【 摘 要 】

We prove the mixed-norm Sobolev estimates for solutions to both divergence and non-divergence form time-dependent Stokes systems with unbounded measurable coefficients having small mean oscillations with respect to the spatial variable in small cylinders. As a special case, our results imply Caccioppoli type inequalities for the Stokes systems with variable coefficients. A new epsilon-regularity criterion for Leray-Hopf weak solutions of Navier-Stokes equations is also obtained as a consequence of our regularity results, which in turn implies some borderline cases of the well-known Serrin's regularity criterion. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free