On Mixed Pressure-Velocity Regularity Criteria to the Navier-Stokes Equations in Lorentz Spaces

作     者：Hugo BEIRAO da VEIGA Jiaqi YANG Hugo BEIRÃO da VEIGA;Jiaqi YANG

作者机构：Department of MathematicsPisa UniversityPisa Italy School of Mathematicsand StatisticsNorthwestern Polytechnical UniversityXi'an 710129China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2021年第42卷第1期

页      面：1-16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 FCT(Portugal)under the project UIDB/MAT/04561/2020 the Fundamental Research Funds for the Central Universities under grant G2019KY05114 

主　　题：Navier-Stokes equations Pressure≌square velocity Regularity criteria Lorentz spaces 

摘      要：In this paper the authors derive regular criteria in Lorentz spaces for LerayHopf weak solutions v of the three-dimensional Navier-Stokes equations based on the formal equivalence relationπ≌|v|^(2),whereπdenotes the fluid pressure and v denotes the fluid *** is called the mixed pressure-velocity problem(the P-V problem for short).It is shown that if(π/(e-^|(x)|^(2)+|v|^(θ)∈L^(p)(0,T;L^(q,∞)),where 0≤θ≤1 and 2/p+3/q=2-θ,then v is regular on(0,T].Note that,ifΩ,is periodic,e^(-|x|)^(2) may be replaced by a positive *** result improves a 2018 statement obtained by one of the ***,as an integral part of the contribution,the authors give an overview on the known results on the P-V problem,and also on two main techniques used by many authors to establish sufficient conditions for regularity of the so-called Ladyzhenskaya-Prodi-Serrin(L-P-S for short)type.