Stationary Oberbeck–Boussinesq model of generalized Newtonian fluid governed by multivalued partial differential equations

Abstract

A generalization of the Oberbeck–Boussinesq model consisting of a system of steady state multivalued partial differential equations for incompressible, generalized Newtonian of the p-power type, viscous flow coupled with the nonlinear heat equation is studied in a bounded domain. The existence of a weak solution is proved by combining the surjectivity method for operator inclusions and a fixed point technique.

Keywords:

• Generalized Newtonian fluid
• Oberbeck–Boussinesq model
• multivalued boundary conditions
• hemivariational inequality

AMS Subject Classifications:

• 76D05
• 47J20
• 49J40
• 35Q30

Acknowledgements

The authors would like to thank the anonymous referee for his/her helpful comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme [grant agreement number 295118]; the National Science Center of Poland under the Maestro [project number DEC-2012/06/A/ST1/00262]; the International Project co–financed by the Ministry of Science and Higher Education of Republic of Poland [grant number W111/7.PR/2012].