Classical ideal fluid motion is described by Euler and Navier-Stokes equations. For real fluids, their motions are more complicated and governed by Euler and Navier-Stokes equations coupled with various constitutive equations. We study viscoelastic models whose motions are
carried out by the competition between the kinetic energies and internal elastic energies. The deformation tensor plays an essential role in our studies. We will present how to use the heuristics coming from the special
structure of the deformation tensor to establish the global well-posedness results for several viscoelastic models, but will focus on a 2D Strain-Rotation model.