典型文献
ON CONTINUATION CRITERIA FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS IN LORENTZ SPACES
文献摘要：
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 equations.First,it is shown that there exists a positive constant ε such 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∞(R3)),u ∈ Lp,∞(0,T;Lq,∞(R3))and||u||Lp,∞(0,T;Lq,∞(R3))≤ε,with 2/p+3/q=1,q＞3;(0.1)(2)λ＜3μ,ρ ∈ L∞(0,T;L∞(R3)),θ ∈ Lp,∞(0,T;Lq,∞(R3))and||θ||Lp,∞(0,T;Lq,∞(R3))≤ε,with 2/p+3/q=2,q＞3/2.(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 fluid.Second,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/q1+1/q2+1/q3=1(1＜qi＜∞)and(1.17),then limsup(||ρ||L∞(0,t;L∞(R3))+||u||Lp(0,t;L11L22L33(R3)))=∞;(0.3)t→T*(2)letting the pair(p,(q))satisfy 2/p+1/q1+1/q2+1/q3=2(1＜qi＜∞)and(1.17),then lim sup(||ρ||L∞(0,t;L∞(w))+||θ||Lp(0,t;Lq11Lq22 Lq33(R3)))=∞,(λ＜3μ).(0.4)t→T*Third,without the condition on ρ in(0.1)and(0.3),the results also hold for the 3D non-homogeneous incompressible Navier-Stokes equations.The appearance of a vacuum in these systems could be allowed.
文献关键词：
中图分类号：
作者姓名：
Yanqing WANG;Wei WEI;Gang WU;Yulin YE
作者机构：
Department of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou 450002,China;Center for Nonlinear Studies,School of Mathematics,Northwest University,Xi'an 710127,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;School of Mathematics and Statistics,Henan University,Kaifeng 475004,China
文献出处：
引用格式：
[1]Yanqing WANG;Wei WEI;Gang WU;Yulin YE-.ON CONTINUATION CRITERIA FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS IN LORENTZ SPACES)[J].数学物理学报（英文版）,2022(02):671-689
A类：
CONTINUATION,CRITERIA,EQUATIONS,LORENTZ,SPACES,q1+1,q2+1,limsup,L11L22L33,letting,Lq11Lq22,Lq33
B类：
FOR,THE,FULL,COMPRESSIBLE,NAVIER,STOKES,In,this,paper,derive,several,new,sufficient,conditions,breakdown,strong,solutions,both,heat,conducting,Navier,Stokes,nonhomogeneous,incompressible,equations,First,shown,that,there,exists,positive,constant,such,full,can,extended,beyond,provided,one,following,two,holds,R3,Lp,p+3,To,best,our,knowledge,first,continuation,theorem,allowing,direction,Lorentz,spaces,fluid,Second,establish,some,blow,criteria,anisotropic,Lebesgue,finite,assuming,pair,satisfies,p+1,qi,then,satisfy,Third,without,results,also,appearance,vacuum,these,systems,could,allowed
AB值：
0.431533
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