Weak solutions for a class of non-Newtonian fluids with energy transfer (Q1586145)
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scientific article; zbMATH DE number 1530299
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak solutions for a class of non-Newtonian fluids with energy transfer |
scientific article; zbMATH DE number 1530299 |
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Weak solutions for a class of non-Newtonian fluids with energy transfer (English)
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13 March 2001
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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.
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multivalued functions
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variational inequality
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continuous dependence on data
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nonlinear convection
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temperature-dependent coefficients
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non-Newtonian fluids
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energy dissipation
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variational formulation
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existence
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weak solution
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Sobolev spaces
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fixed point technique
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Galerkin method
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Yosida approximation
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Lagrange multipliers
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uniqueness
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