Hele-Shaw approximation for resin transfer molding

A Hele-Shaw flow is studied as the limit of a Stokes flow. The velocity fields associated to each fluid solve a fluid dynamic problem with time dependent domain. The moving boundary formulation is based on a pseudo-concentration equation. Some existence of solution of this set of equations is given using the classical Leary-Schauder Theorem and the use of space-time integrated least square method for the transport equation.