On existence of a classical solution to a generalized Kelvin–Voigt model

We consider a two-dimensional generalized Kelvin-Voigt model describing a motion of a compressible viscoelastic body.We establish the existence of a unique classical solution to such a model in the spatially periodic setting.The proof is based on Meyers' higher integrability estimates that guarantee the Hölder continuity of the gradient of velocity and displacement.