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Conduction-convection problems with change of phase. (English) Zbl 0593.35085
In the usual simplest formulation of free boundary problems one considers only the conduction, here a formulation is studied where also convective motions are taking into account. Two problems are studied: a ground freezing one, in which the water is subjected to Darcy’s law, and a two phases stationary Stefan problem, where the motion of water is governed by the Navier-Stokes equations. Results on regularity of the solutions and of the free boundary are given in both cases.
Reviewer: M.Biroli

##### MSC:
 35R35 Free boundary problems for PDEs 35B65 Smoothness and regularity of solutions to PDEs 35Q30 Navier-Stokes equations 76R99 Diffusion and convection 80A20 Heat and mass transfer, heat flow (MSC2010)
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