Geodesic
On classical solvability of the multidimensional Stefan problem for convective motion of a~viscous incompressible fluid
Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 1-17

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The Stefan problem for a quasilinear parabolic equation is considered. Convective motions in the fluid phase are described by the Navier–Stokes system. The existence of a smooth solution locally in time is proved. Bibliography: 15 titles 
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     title = {On classical solvability of the multidimensional {Stefan} problem for convective motion of a~viscous incompressible fluid},
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B. V. Bazalii; S. P. Degtyarev. On classical solvability of the multidimensional Stefan problem for convective motion of a~viscous incompressible fluid. Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/SM_1988_60_1_a0/