Consiglieri, Luisa Weak solutions for a class of non-Newtonian fluids with energy transfer. (English) Zbl 0974.35090 J. Math. Fluid Mech. 2, No. 3, 267-293 (2000). The author studies a nonlinear convection problem with temperature-dependent coefficients for a rather general class of non-Newtonian fluids with energy dissipation. After introducing a variational formulation of the problem, the author proves the existence of a non-unique weak solution in Sobolev spaces by the fixed point technique, employing Galerkin method, Yosida approximation, and Lagrange multipliers for the associated generalized Navier-Stokes system. The uniqueness of the solution is guaranteed after prescribing the diffusion coefficient and convective as well as dissipative terms. Reviewer: Oleg Titow (Berlin) Cited in 23 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76A05 Non-Newtonian fluids 76M30 Variational methods applied to problems in fluid mechanics 80A20 Heat and mass transfer, heat flow (MSC2010) 76R10 Free convection Keywords:multivalued functions; variational inequality; continuous dependence on data; nonlinear convection; temperature-dependent coefficients; non-Newtonian fluids; energy dissipation; variational formulation; existence; weak solution; Sobolev spaces; fixed point technique; Galerkin method; Yosida approximation; Lagrange multipliers; uniqueness PDFBibTeX XMLCite \textit{L. Consiglieri}, J. Math. Fluid Mech. 2, No. 3, 267--293 (2000; Zbl 0974.35090) Full Text: DOI