ENERGY CONSERVATION FOR SOLUTIONS OF INCOMPRESSIBLE VISCOELASTIC FLUIDS

• 作者: Yiming HE Ruizhao ZI
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（4）
• 页码范围: 1287-1301
• 页数: 15页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.04.016

摘要

Some sufficient conditions of the energy conservation for weak solutions of in-compressible viscoelastic flows are given in this paper.First,for a periodic domain in R3,and the coefficient of viscosity μ =0,energy conservation is proved for u and F in certain Besov spaces.Furthermore,in the whole space R3,it is shown that the conditions on the velocity u and the deformation tensor F can be relaxed,that is,u ∈ B1/33,c(N),and F ∈ B1/33,∞.Finally,when μ ＞ 0,in a periodic domain in Rd again,a result independent of the spacial dimension is established.More precisely,it is shown that the energy is conserved for u ∈ LT (0,T;Ls (Ω))for any 1/r +1/s ≤ 1/2,with s ≥ 4,and F ∈ Lm(0,T;Ln(Ω)) for any 1/m + 1n ≤1/2,with n ≥ 4.