Energy Conservation For Solutions Of The Incompressible Viscoelastic Fluids

In this thesis,we give some sufficient conditions of the energy conservation for weak solutions of the incompressible viscoelastic flows.First in the case of periodic domain in R3,and the coefficient of viscosity ?=0,we show energy conservation for u and F in certain Besov spaces.Furthermore,in the whole space R3,we prove that the conditions on the velocity u and the deformation tensor F can be relaxed,i.e.,u?B3,c(N),1/3,and F?B3,?,1/3.When ?>0,in a pariodic domain in Rd,We obtain a result independent of dimension.More precisely,we find that the energy is conserved for u?LT(0,T;L8(?))for any 1/r+1/s?1/2,with s?4.and F ? Lm(0,T;Ln((?))for any 1/m+1/n?1/2,with n?4.