ON EXISTENCE OF A CLASSICAL SOLUTION TO A GENERALIZED KELVIN-VOIGT MODEL

Abstract

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 Holder continuity of the gradient of velocity and displacement.

Keywords

• Kelvin-Voigt model
• regularity
• classical solution
• large-data and long-time behavior