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 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, \(u \in B_{3,c(\mathbb{N})}^{{1 \over 3}}\), and \(F \in B_{3,\infty }^{{1 \over 3}}\). 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^r (0, T; L^s (Ω)) for any \({1 \over r} + {1 \over s} \leqslant {1 \over 2}\), with s ⩾ 4, and F ∈ L^m(0, T; Lⁿ(Ω)) for any \({1 \over m} + {1 \over n} \leqslant {1 \over 2}\), with n ⩾ 4.

给出了不可压缩粘弹性流动弱解能量守恒的一些充分条件。首先，对于 ℝ ^{3 中}的周期域，并且粘度系数μ = 0，在某些 Besov 空间中证明了u和F 的能量守恒。此外，在整个空间 ℝ ^{3 中}，表明速度u和变形张量F 的条件可以放宽，即\(u \in B_{3,c(\mathbb{N})}^ {{1 \over 3}}\)和\(F \in B_{3,\infty }^{{1 \over 3}}\)。最后，当μ > 0 时，在 ℝ ^d的周期域中再次，建立了独立于空间维度的结果。更确切地说，示出了能量守恒为Ü ∈大号^{- [R}（0，Ť ;大号^小号（Ω）），用于任何\（{1 \超过R} + {1 \超过S} \ leqslant {1 \过2}\) , s ⩾ 4, 并且F ∈ L ^m (0, T ; L ⁿ (Ω)) 对于任何\({1 \over m} + {1 \over n} \leqslant {1 \over 2 }\)，n ⩾ 4。