TY - JOUR
T1 - The Stefan Problem with Nonlinear Convection
AU - Wang Xuefeng
JO - Journal of Partial Differential Equations
VL - 4
SP - 66
EP - 86
PY - 1992
DA - 1992/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5755.html
KW - Stefan problem
KW -  nonlinear convection
KW -  penalty method
KW -  compactness arguments
AB -  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.