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# Rotation-strain decomposition for the incompressible viscoelasticity in two dimensions

• In this paper, we revisit the 2D rotation-strain model which was derived in [14] for the motion of incompressible viscoelastic materials and prove its global well-posedness theory without making use of the equation of the rotation angle. The proof relies on a new identity satisfied by the strain matrix. The smallness assumptions are only imposed on the $H^2$ norm of initial velocity field and the initial strain matrix, which implies that the deformation tensor is allowed being away from the equilibrium of 2 in the maximum norm.
Mathematics Subject Classification: Primary: 76D03, 76D09; Secondary: 35M10.

 Citation:

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