On the stationary Boussinesq-Stefan problem with constitutive power-laws

• Autor(a) principal: Rodrigues, José Francisco
• Data de Publicação: 1998
• Outros Autores: Urbano, José Miguel
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/4667; https://doi.org/10.1016/s0020-7462(97)00041-3
• topic: free boundary problems; Boussinesq-Stefan problem; non-Newtonian flow; thermomechanics of solidification; p-Laplacian; variational inequalities

We discuss the existence of weak solutions to a steady-state coupled system between a two-phase Stefan problem, with convection and non-Fourier heat diffusion, and an elliptic variational inequality traducing the non-Newtonian flow only in the liquid phase. In the Stefan problem for the p-Laplacian equation the main restriction comes from the requirement that the liquid zone is at least an open subset, a fact that leads us to search for a continuous temperature field. Through the heat convection coupling term, this depends on the q-integrability of the velocity gradient and the imbedding theorems of Sobolev. We show that the appropriate condition for the continuity to hold, combining these two powers, is pq> n. This remarkably simple condition, together with q> 3n/(n + 2), that assures the compactness of the convection term, is sufficient to obtain weak solvability results for the interesting space dimension cases n = 2 and n = 3.