EXISTENCE OF LARGE-DATA GLOBAL WEAK SOLUTIONS TO A MODEL OF A STRAIN-LIMITING VISCOELASTIC BODY

We prove the existence of a unique large-data global-in-time weak solution to a class of models of the form u(tt) = div T + f for viscoelastic bodies exhibiting strain-limiting behaviour, where the constitutive equation, relating the linearised strain tensor epsilon(u) to the Cauchy stress tensor T, is assumed to be of the form epsilon(u(t))+ alpha epsilon(u) = F (T), where we define F (T) = (1+ vertical bar T vertical bar(a))(-1/a) T, for constant parameters alpha is an element of (0, infinity) and a is an element of (0, infinity), in any number d of space dimensions, with periodic boundary conditions. The Cauchy stress T is shown to belong to L-1 (Q)(dxd) over the space-time domain Q. In particular, in three space dimensions, if a is an element of (0, 2/7), then in fact T is an element of L1+delta (Q)(dxd) for a delta > 0, the value of which depends only on a.