An Existence Theorem for the Multifluid Navier-Stokes Problem

Existence of a weak solution of the Navier-Stokes problem describing a multifluid flow is proved. The velocity fields associated to each fluid solves the Navier-Stokes equations in a time-dependent domain. Classical immiscibility conditions on the varying fluids interfaces are taken into account by a new formulation of the problem. This formulation was introduced in [5] and used in numerical computations. This paper follows a previous one where an existence theorem for Stokes multifluid problems was derived ([7]).