On 2D Viscoelasticity with Small Strain

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.