Well-posedness for the classical Stefan problem and the zero surface tension limit

Details Well-posedness for the classical Stefan problem and the zero surface tension limit Well-posedness for the classical Stefan problem and the zero surface tension limit

2011-12-26

arxiv.org/abs/1112.5817v1

Mathematics

Analysis of PDEs

28 pages

Scientific paper

We develop a framework for a {\em unified} treatment of well-posedness for the Stefan problem with and without surface tension. In the absence of surface tension, we provide new estimates for the regularity of the moving free-surface. We construct solutions as a limit of a carefully chosen sequence of approximate solutions to our so-called $\kappa $-problem, in which moving surface is regularized and the boundary condition is modified. We conclude by proving that solutions of the Stefan problem with positive surface tension $\sigma$ converge to solutions of the classical Stefan problem as $\sigma\to0$.

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