EXISTENCE OF WEAK SOLUTIONS FOR PARTICLE-LADEN FLOW WITH SURFACE TENSION

We prove the existence of solutions for a coupled system modeling the flow of a suspension of fluid and negatively buoyant non-colloidal particles in the thin film limit. The equations take the form of a fourth-order nonlinear degenerate parabolic equation for the film height h coupled to a second-order degenerate parabolic equation for the particle density psi. We prove the existence of physically relevant solutions, which satisfy the uniform bounds 0 <= psi/h <= 1 and h >= 0.