ENERGY CONSERVATION FOR SOLUTIONS OF INCOMPRESSIBLE VISCOELASTIC FLUIDS  

作　　者：Yiming HE Ruizhao ZI 何一鸣;訾瑞昭(School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China;School of Mathematics and Statistics&Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,China)

机构地区：[1]School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China [2]School of Mathematics and Statistics&Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,China

出　　处：《Acta Mathematica Scientia》2021年第4期1287-1301,共15页数学物理学报（B辑英文版）

基　　金：R.Zi is partially supported by the National Natural Science Foundation of China(11871236 and 11971193);the Natural Science Foundation of Hubei Province(2018CFB665);the Fundamental Research Funds for the Central Universities(CCNU19QN084).

摘　　要：Some sufficient conditions of the energy conservation for weak solutions of incompressible viscoelastic flows are given in this paper.First,for a periodic domain in R^(3),and the coefficient of viscosity μ=0,energy conservation is proved for u and F in certain Besovs paces.Furthermore,in the whole space R^(3),it is shown that the conditions on the velocity u and the deformation tensor F can be relaxed,that is,u∈B_(3,c(N))^(1/3),and F∈B_(3,∞)^(1/3).Finally,when μ>0,in a periodic domain in R^(d) again,a result independent of the spacial dimension is established.More precisely,it is shown that the energy is conserved for u∈L^(T)(0,T;L^(n)(Ω))for any 1/r+1/s≤1/2,with s≥4,and F∈L^(m)(0,T;L^(n)(Ω))for any 1/m+1/n≤1/2,with n≥4.

关 键 词：Incompressible viscoelastic fluids weak solutions energy conservation 

分 类 号：O357.1[理学—流体力学]