ON CONTINUATION CRITERIA FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS IN LORENTZ SPACES

作     者：Yanqing WANG Wei WEI Gang WU Yulin YE 王艳青;魏巍;吴刚;叶嵎林

作者机构：Department of Mathematics and Information ScienceZhengzhou University of Light IndustryZhengzhou 450002China Center for Nonlinear StudiesSchool of MathematicsNorthwest UniversityXi’an 710127China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China School of Mathematics and StatisticsHenan UniversityKaifeng 475004China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2022年第42卷第2期

页      面：671-689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 NationalNatural Science Foundation of China(11971446,12071113,11601423,11771352,11871057,11771423,11671378,11701145) Project funded by China Postdoctoral Science Foundation(2020M672196) 

主　　题：Navier-Stokes equations strong solutions regularity 

摘      要：In this paper,we derive several new sufficient conditions of the non-breakdown of strong solutions for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes ***,it is shown that there exists a positive constantεsuch that the solution(ρ,u,θ)to the full compressible Navier-Stokes equations can be extended beyond t=T provided that one of the following two conditions holds:(1)ρ∈L^(∞)(0,T;L^(∞)(R^(3)),u∈L^(p,∞)(0,T;L^(q,∞)(R^(3)))and ||u||_(L^(p,∞)(0,T;L^(q,∞)(R^(3))))≤ε,with 2/p+3/q=1,q3;(0.1)(2)λ3/2(0.2)To the best of our knowledge,this is the first continuation theorem allowing the time direction to be in Lorentz spaces for the compressible ***,we establish some blow-up criteria in anisotropic Lebesgue spaces for the finite blow-up time T^(*):(1)assuming that the pair(p,q) satisfies 2/p+1/q_(1)+1/q_(2)+1/q_(3)=1(1q_(i)∞)and (1.17),then lim sup_((t→T*))||ρ||_(L^(∞)(0,t;L^(∞)(R^(3))))+||u||_(Lp(0,t;L_(1)^(q_(1))L_(2)^(q_(2))L_(3)^(q_(3))(R^(3)))))=∞;(0.3)(2)letting the pair(p,q)satisfy 2/p+1/q_(1)+1/q_(2)+1/q_(3)=1(1q_(i)∞)and(1.17),then lim sup (t→T*)||ρ||_(L^(∞)(0,t;L^(∞)(R^(3))))+||θ||_(Lp(0,t;L_(1)^(q_(1))L_(2)^(q_(2))L_(3)^(q_(3))(R^(3)))))=∞=∞,(λ3μ).(0.4)Third,without the condition on p in(0.1)and(0.3),the results also hold for the 3 D nonhomogeneous incompressible Navier-Stokes *** appearance of a vacuum in these systems could be allowed.