CLASSICAL SOLVABILITY OF THE TWO-PHASE STEFAN PROBLEM IN A VISCOUS INCOMPRESSIBLE FLUID FLOW
Yoshiaki Kusaka, Atusi Tani · Mathematical Models and Methods in Applied Sciences · 2002
In this paper we study the two-phase Stefan problem for a viscous incompressible fluid which is a model of melting a solid to a liquid or of soldificating a liquid to a solid with a liquid flowing. The unique solvability is established in Hölder spaces locally in time. The method of the proof is rather standard, however the result obtained is completely new: the existence in the Hölder spaces with the same Hölder exponents as the data and the uniqueness also in the same Hölder spaces.