, Volume 52, Issue 1, pp 19–36 | Cite as

On stationary thermo-rheological viscous flows

  • Stanislav N. Antontsev
  • José F. Rodrigues


We study the system of equations describing a stationary thermoconvective flow of a non-Newtonian fluid. We assume that the stress tensor S has the form

\(\displaystyle \mathbf{S}=-P\mathbf{I}+\left( \mu (\theta )+\tau (\theta ){|\mathbf{D(u)}|}^{p(\theta )-2}\right) {\mathbf{D(u)}}, \)

where u is the vector velocity, P is the pressure, θ is the temperature and μ ,p and τ are the given coefficients depending on the temperature. D and I are respectively the rate of strain tensor and the unit tensor. We prove the existence of a weak solution under general assumptions and the uniqueness under smallness conditions.

Keywords: Non-Newtonian fluids, Nonlinear thermal diffusion equations, Heat and mass transfer

Mathematics Subject Classification (2000): 76A05, 76D07, 76E30, 35G15


Weak Solution Stokes Problem Sobolev Embedding Unique Weak Solution Lavrentiev Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Stanislav N. Antontsev
    • 1
  • José F. Rodrigues
    • 2
  1. 1.Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal, Tel.: 00351-275 319 757, Fax: 00351-275 329 972 
  2. 2.CMUC and Universidade de Lisboa/CMAF, Av. Prof. Gama Pinto 2, 1649-003 LisboaPortugal

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