Abstract: | We study a quasi-static incompressible flow of Bingham type with constituent law \ \begin{array}{ll} T = p\left| {\cal E}u\right| ?{p-2}{\cal E}u+\beta \frac{{\cal E}u}{\left| {\cal E}u\right| } & \text{if }{\cal E}u\neq 0, \\ \left| T\right| \leq \beta & \text{if }{\cal E}u = 0, \end{array} \] T = p∣?u∣p-2?u+β ?u ∣?u∣ if ?u≠0, ∣T∣?β if ?u = 0, where p≥2 and β>0. Here ?u denotes the strain velocity and T the corresponding stress. The problem admits a variational formulation in the sense that the velocity field u minimizes the energy I(u) = ∫Ω∣?u∣p+β∣?u∣dx in the space {v∈H1,p(Ω,?n): div v = 0} subject to appropriate boundary conditions. We then show smoothness of u on the set {x∈Ω: ?u≠0}. |