The Stefan Problem with Nonlinear Convection (Journal of Partial Differential Equations, 2020)
In this paper, we consider the time dependent Stefan problem with convection in the fluid phase governed by the Navier-Stokes equation and with adherence of the fluid on the lateral 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 the application of various compactness arguments.
Keywords: Stefan problem; nonlinear convection; penalty method; compactness arguments