Strong solutions of the equations for viscoelastic fluids in some classes of large data

We study the existence and uniqueness of global strong solutions to equations an incompressible viscoelastic fluid in a spatially periodic domain, show that unique solution exists globally time if initial deformation velocity are small for given physical parameters. In particular, can be large elasticity coefficient. Our result mathematically verifies prevent formation singularities with velocity, thus playing similar role viscosity preventing viscous flows. Moreover, perturbation zero around rest state, we find, as coefficient or goes infinity, any straight line segment l0 consisted particles after being bent by perturbation, will turn into is parallel has same length l0. motion approximated linear pressureless Lagrangian coordinates, even when large.