The steady state Stefan problem with convection

For steady-state Stefan problems with convection in the fluid phase governed by either the Stokes equations or the Navier Stokes equations, and with adherence of the fluid on all boundaries, the existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation together with application of various compactness arguments.This research was supported in part by the National Science Foundation and the Consiglio Nazionale delle Ricerche.