The steady Navier–Stokes/energy system with temperature‐dependent viscosity—Part 1: Analysis of the continuous problem |
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| Authors: | Carlos E. Pérez Jean‐Marie Thomas Serge Blancher René Creff |
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| Affiliation: | 1. Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160‐C, Concepción, Chile;2. Laboratoire de Mathématiques Appliquées, Université de Pau, BP 1155, Pau 64013, France;3. Laboratoire de Transferts Thermiques, Université de Pau, France, Hélioparc, Av. Pres. Angot, Pau 64000, France |
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| Abstract: | In this first part we propose and analyse a model for the study of two‐dimensional incompressible Navier–Stokes equations with a temperature‐dependent viscosity. The flow is supposed in a mixed convection regime and considers an outflow region, leading to a strongly coupled problem between the Navier–Stokes and energy equations, which will be justified theoretically. The coupling in the continuous problem is treated by an outer temperature fixed point strategy. Existence results for a particular variational formulation follows from this study. Further, a particular uniqueness result for small data is also obtained. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | Navier– Stokes variable viscosity coupled equations |
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