Existence result for a strongly coupled problem with heat convection term and Tresca's law.

Bensedik Ahmed (1) , Boukrouche Mahdi (1)

1 MMCS - Modélisation mathématique, calcul scientifique

We study a problem describing the motion of an incompressible, nonisothermal and non-Newtonian uid, taking into account the heat convection term. The novelty here is that uid viscosity depends on the temperature, the velocity of the uid, and also of the deformation tensor, but not explicitly. The boundary conditions take into account the slip phenomenon on a part of the boundary of the domain. By using the notion of pseudo-monotone operators and xed point Theorem we prove an existence result of its weak solution.

Mots clés: Non-Newtonian fluid; Non-isothermal fluid; Tresca fluid-solid conditions; Pseudo-monotone operators; Schauder point fixed Theorem.; Schauder point fixed Theorem

Domaines: Equations aux dérivées partielles [math.AP]

Bensedik Ahmed, Boukrouche Mahdi. Existence result for a strongly coupled problem with heat convection term and Tresca's law.. Journal of Advanced Research in Differential Equations, 2011, 3 (3), pp.33-53. ⟨hal-00863344⟩