Planar flows of incompressible heat-conducting shear-thinning fluids — existence analysis

Miroslav Bulíček; Oldřich Ulrych

Applications of Mathematics (2011)

  • Volume: 56, Issue: 1, page 7-38
  • ISSN: 0862-7940

Abstract

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We study the flow of an incompressible homogeneous fluid whose material coefficients depend on the temperature and the shear-rate. For large class of models we establish the existence of a suitable weak solution for two-dimensional flows of fluid in a bounded domain. The proof relies on the reconstruction of the globally integrable pressure, available due to considered Navier’s slip boundary conditions, and on the so-called L ∞ -truncation method, used to obtain the strong convergence of the velocity gradient. The important point of the approach consists in the choice of an appropriate form of the balance of energy.

How to cite

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Bulíček, Miroslav, and Ulrych, Oldřich. "Planar flows of incompressible heat-conducting shear-thinning fluids — existence analysis." Applications of Mathematics 56.1 (2011): 7-38. <http://eudml.org/doc/116502>.

@article{Bulíček2011,
abstract = {We study the flow of an incompressible homogeneous fluid whose material coefficients depend on the temperature and the shear-rate. For large class of models we establish the existence of a suitable weak solution for two-dimensional flows of fluid in a bounded domain. The proof relies on the reconstruction of the globally integrable pressure, available due to considered Navier’s slip boundary conditions, and on the so-called $L^\infty $-truncation method, used to obtain the strong convergence of the velocity gradient. The important point of the approach consists in the choice of an appropriate form of the balance of energy.},
author = {Bulíček, Miroslav, Ulrych, Oldřich},
journal = {Applications of Mathematics},
keywords = {heat-conducting fluid; non-Newtonian fluid; shear-thinning fluid; existence; weak solution; suitable weak solution; $L^\{\infty \}$-truncation method; balance of energy; heat-conducting fluid; non-Newtonian fluid; shear-thinning fluid; suitable weak solution; -truncation method; balance of energy},
language = {eng},
number = {1},
pages = {7-38},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Planar flows of incompressible heat-conducting shear-thinning fluids — existence analysis},
url = {http://eudml.org/doc/116502},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Bulíček, Miroslav
AU - Ulrych, Oldřich
TI - Planar flows of incompressible heat-conducting shear-thinning fluids — existence analysis
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 1
SP - 7
EP - 38
AB - We study the flow of an incompressible homogeneous fluid whose material coefficients depend on the temperature and the shear-rate. For large class of models we establish the existence of a suitable weak solution for two-dimensional flows of fluid in a bounded domain. The proof relies on the reconstruction of the globally integrable pressure, available due to considered Navier’s slip boundary conditions, and on the so-called $L^\infty $-truncation method, used to obtain the strong convergence of the velocity gradient. The important point of the approach consists in the choice of an appropriate form of the balance of energy.
LA - eng
KW - heat-conducting fluid; non-Newtonian fluid; shear-thinning fluid; existence; weak solution; suitable weak solution; $L^{\infty }$-truncation method; balance of energy; heat-conducting fluid; non-Newtonian fluid; shear-thinning fluid; suitable weak solution; -truncation method; balance of energy
UR - http://eudml.org/doc/116502
ER -

References

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