Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling ν ( p , · ) → + ∞ as p → + ∞

M. Bulíček; Josef Málek; Kumbakonam R. Rajagopal

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 2, page 503-528
  • ISSN: 0011-4642

Abstract

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Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities and in order to explain the main idea in as simple a manner as possible, we restrict ourselves to a discussion of the spatially periodic problem.

How to cite

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Bulíček, M., Málek, Josef, and Rajagopal, Kumbakonam R.. "Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling $\nu (p, \cdot ) \rightarrow + \infty $ as $p \rightarrow +\infty $." Czechoslovak Mathematical Journal 59.2 (2009): 503-528. <http://eudml.org/doc/37937>.

@article{Bulíček2009,
abstract = {Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities and in order to explain the main idea in as simple a manner as possible, we restrict ourselves to a discussion of the spatially periodic problem.},
author = {Bulíček, M., Málek, Josef, Rajagopal, Kumbakonam R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {\{existence; weak solution; incompressible fluid; pressure-dependent viscosity; shear-dependent viscosity; spatially periodic problem\}; existence; weak solution; incompressible fluid; pressure-dependent viscosity; shear-dependent viscosity; spatially periodic problem},
language = {eng},
number = {2},
pages = {503-528},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling $\nu (p, \cdot ) \rightarrow + \infty $ as $p \rightarrow +\infty $},
url = {http://eudml.org/doc/37937},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Bulíček, M.
AU - Málek, Josef
AU - Rajagopal, Kumbakonam R.
TI - Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling $\nu (p, \cdot ) \rightarrow + \infty $ as $p \rightarrow +\infty $
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 503
EP - 528
AB - Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities and in order to explain the main idea in as simple a manner as possible, we restrict ourselves to a discussion of the spatially periodic problem.
LA - eng
KW - {existence; weak solution; incompressible fluid; pressure-dependent viscosity; shear-dependent viscosity; spatially periodic problem}; existence; weak solution; incompressible fluid; pressure-dependent viscosity; shear-dependent viscosity; spatially periodic problem
UR - http://eudml.org/doc/37937
ER -

References

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