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 ...
