On Mixed Pressure-Velocity Regularity Criteria to the Navier-stokes Equations in Lorentz Spaces,Part Ⅱ:The Non-slip Boundary Value Problem

• 作者: Hugo BEIR(A)O DA VEIGA Jiaqi YANG
• 来源期刊: 数学年刊B辑（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 51-58
• 页数: 8页
• 语种: 英文
• DOI: 10.1007/s11401-022-0303-z

摘要

This paper is a continuation of the authors recent work[Beir(a)o da Veiga,H.and Yang,J.,On mixed pressure-velocity regularity criteria to the Navier-Stokes equations in Lorentz spaces,Chin.Ann.Math.,42(1),2021,1-16],in which mixed pressure-velocity criteria in Lorentz spaces for Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations,in the whole space R3 and in the periodic torus T3,are established.The purpose of the present work is to extend the result of mentioned above to smooth,bounded domains Ω,under the non-slip boundary condition.Let πr denote the fluid pressure and v the fluid velocity.It is shown that if π/(1+|v|θ) ∈ Lp(0,T;Lq,∞(Ω)),where 0 ≤ θ ≤ 1,and 2/p + 3/q =2-θ with p ≥ 2,then v is regular on Ω× (0,T].