| Title | STEADY-STATE THERMAL VISCOUS INCOMPRESSIBLE FLOWS WITH CONVECTIVE-RADIATIVE EFFECTS AND A NONLOCAL COULOMB FRICTION LAW |
| Publication Type | Journal Article |
| Year of Publication | 2006 |
| Authors | Consiglieri, L |
| Secondary Title | Communications in Applied Analysis |
| Volume | 10 |
| Issue | 4 |
| Start Page | 505 |
| Pagination | 516 |
| Date Published | 12/2006 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 35D05, 35J55, 49J40, 74M10, 76A05, 80A20 |
| Abstract | We deal with a coupled system of elliptic motion and energy equations motivated by the thermal flow of a class of non-Newtonian fluids. A nonlocal Coulomb friction condition on a part of the liquid-solid boundary is taken into account. On this part of the boundary it is also considered a convective-radiative heat transfer related to the frictional work. The existence of a weak solution constitutes the main result of the present work which proof is based on a fixed point argument for multivalued mappings. The nonlinear boundary conditions as well as the energy dependent viscosities and the thermal conductivity are the crucial contribution on the interdependence on the fluid velocity vector, the stress tensor and the internal energy. The mathematical framework of the paper includes the classical monotone theory on elliptic equations, the duality theory of convex analysis in order to describe the Lagrange multipliers; and the L1 -theory on partial differential equations due to the existence of the Joule effect. |
| URL | http://www.acadsol.eu/en/articles/10/4/5.pdf |
| Short Title | Steady-State Thermal Viscous Incompressible Flows |
| Refereed Designation | Refereed |
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