Quasi-variational solutions to thick flows

Formulating the flow of thick fluids, with a variable threshold on the absolute value of the deformation rate tensor depending on the solution, as an evolution quasi-variational inequality, we show the existence of strong and weak solutions in different cases. The results are based on new extensions on the uniqueness of weak solutions and the respective Lagrange multipliers associated to the variational inequalities for the Navier–Stokes equations with constraints on the derivatives. This is a joint work with Lisa Santos.
The talk is dedicated to Vsevolod Alekseevich Solonnikov, in memoriam.