Friction boundary conditions on thermal incompressible viscous flows

Annali di Matematica Pura ed Applicata

Volumn 187, Issue 4, 2008, Pages 647-665

  Consiglieri, L ^a  

^a UNIVERSITY OF LISBON   (Portugal)

Author keywords

Convective heat transfer; Friction laws; Lagrange multipliers; Subdifferential; Thermal non Newtonian fluids

Indexed keywords

EID: 45749101739     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/s10231-007-0060-3     Document Type: Article

References (23)

1. Antontsev, S.N., Kazhikhov, A.V., Monakhov, V.N.: Boundary value problems in mechanics of nonhomogeneous fluids. Studies in Mathematics and its Applications, vol. 22, North-Holland, 1990. Translation of Russian. Novosibirsk: Nauka (1983)
2. Beirão da Veiga H. (2005). On the regularity of flows with Ladyzhenskaya shear-dependent viscosity and slip or nonslip boundary conditions. Comm. Pure Appl. Math. 58: 552-577
3. Boccardo L. and Gallouet T. (1989). Non-linear elliptic and parabolic equations involving measure. J. Funct. Anal. 87: 149-169
4. Brézis H. (1973). Operateurs Maximaux Monotones. North-Holland, Amsterdam
5. Boukrouche M. and Lukaszewicz G. (2003). Asymptotic analysis of solutions of a thin-film lubrification problem with Coulomb fluid-solid interface law. Int. J. Eng. Sci. 41: 521-537
6. Cioranescu, D.: Quelques exemples de fluides Newtoniens generalisés. In: Rodrigues J.F., Sequeira A. (eds.) Mathematical topics in fluid mechanics. Pitman Res. Notes in Math. Harlow, Longman 1-31 (1992)
7. Consiglieri L. (2000). Weak solutions for a class of non-Newtonian fluids with energy transfer. J. Math. Fluid Mech. 2: 267-293
8. 1 data. Application to the H-convergence of quasi-linear parabolic equations. Annali Mat. Pura Appl. 170(1): 207-240
9. Ekeland I. and Temam R. (1974). Analyse convexe et problèmes variationnels. Dunod et Gauthier-Villars, Paris
10. Glicksberg I.L. (1952). A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Am. Math. Soc. 3: 170-174
11. Hadrian U. and Panagiotopoulos P.D. (1978). Superpotential flow problems and application to metal forming processes with friction boundary conditions. Mech. Res. Comm. 5: 257-267
12. Herreros, M.I., González, E., Pastor, M., Quecedo, M., Fernández Merodo, J.A.: Modelos discretos y continuos para la modelización de deslizamientos rápidos de ladera. In: Proceedings of Congresso de Métodos Computacionais em Engenharia. Mota Soares, C.A., et al. (eds.) LNEC (2004) Lisboa
13. Hutter K. and Rajagopal K.R. (1994). On flows of granular materials. Continuum Mech. Thermodyn. 6: 81-139
14. Jäger W. and Mikelić A. (2001). On the roughness-induced effective boundary conditions for an incompressible viscous flow. J. Diff. Eq. 170: 96-122
15. Kikuchi N. and Oden J.T. (1988). Contact problems in elasticity. Siam, Philadelphia
16. Lions J.L. (1969). Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod et Gauthier- Villars, Paris
17. Málek J., Nečas J., Rokyta M. and Rǔž ička M. (1996). Weak and Measure-valued solutions to evolutionary PDEs. Chapman and Hall, London
18. Mohammadi B. and Pironneau O. (1994). Analysis of the K-Epsilon turbulence model. Research in Applied Mathematics. Wiley/Masson, London/Paris
19. Naumann J. and Wulst M. (1979). On evolution inequalities of Bingham type in three dimensions. I. J. Math. Anal. Appl. 68: 211-227
20. 1-data. Nonlinear Anal. 46: 737-755
21. Porzio M.M. and López-Pouso O. (2002). Linear elliptic problems with mixed boundary conditions related to radiation heat transfer. Math. Mod. Meth. Appl. Sci. 12(4): 541-565
22. Rao I.J. and Rajagopal K.R. (1999). The effect of the slip boundary condition on the flow of fluids in a channel. Acta Mech. 135: 113-126
23. Zeidler E. (1990). Nonlinear functional analysis II/B. Springer, New York