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We prove the local in time existence of regular solutions to the system of equations of isothermal viscoelasticity with clamped boundary conditions. We deal with a general form of viscous stress tensor $\mathcal{Z}(F,\dot F)$, assuming a Korn-type condition on its derivative $D_{\dot F}\mathcal{Z}(F, \dot F)$. This condition is compatible with the balance of angular momentum, frame invariance and the Claussius-Duhem inequality. We give examples of linear and nonlinear (in $\dot F$) tensors $\mathcal{Z}$ satisfying these required conditions.

A local existence result for a system of viscoelasticity with physical viscosity