We extend the conventional mode-coupling theory of supercooled liquids to systems under stationary shear flow. Starting from generalized fluctuating hydrodynamics, a nonlinear equation for the intermediate scattering function is constructed. We evaluate the solution numerically for a model of a two dimensional colloidal suspension and find that the structural relaxation time decreases as $\dot{ \gamma}^{ -\nu}$ with an exponent $\nu \leq 1$, where $\dot{ \gamma}$ is the shear rate. The results are in qualitative agreement with recent molecular dynamics simulations. We discuss the physical implications of the results.
Categories: cond-mat.stat-mech