Bipolar barotropic nonnewtonian fluid

Šárka Matušů-Nečasová; Mária Medviďová

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 3, page 467-483
  • ISSN: 0010-2628

Abstract

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The paper describes the special situation of barotropic nonnewtonian fluid, where stress tensor can be written in the form of potentials which depend on e i j and ( ∂ e i j ∂ x k ) . For this case, we prove the existence and uniqueness of weak solution.

How to cite

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Matušů-Nečasová, Šárka, and Medviďová, Mária. "Bipolar barotropic nonnewtonian fluid." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 467-483. <http://eudml.org/doc/247635>.

@article{Matušů1994,
abstract = {The paper describes the special situation of barotropic nonnewtonian fluid, where stress tensor can be written in the form of potentials which depend on $e_\{ij\}$ and $(\frac\{\partial e_\{ij\}\}\{\partial x_k\})$. For this case, we prove the existence and uniqueness of weak solution.},
author = {Matušů-Nečasová, Šárka, Medviďová, Mária},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {barotropic nonnewtonian fluid; bipolar fluid; existence; uniqueness; weak solution; Galerkin method; method of characteristics; a priori estimates; Aubin lemma; stress tensor; existence; uniqueness; weak solution},
language = {eng},
number = {3},
pages = {467-483},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Bipolar barotropic nonnewtonian fluid},
url = {http://eudml.org/doc/247635},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Matušů-Nečasová, Šárka
AU - Medviďová, Mária
TI - Bipolar barotropic nonnewtonian fluid
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 467
EP - 483
AB - The paper describes the special situation of barotropic nonnewtonian fluid, where stress tensor can be written in the form of potentials which depend on $e_{ij}$ and $(\frac{\partial e_{ij}}{\partial x_k})$. For this case, we prove the existence and uniqueness of weak solution.
LA - eng
KW - barotropic nonnewtonian fluid; bipolar fluid; existence; uniqueness; weak solution; Galerkin method; method of characteristics; a priori estimates; Aubin lemma; stress tensor; existence; uniqueness; weak solution
UR - http://eudml.org/doc/247635
ER -

References

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  1. Adams R.A., Sobolev spaces, Academic Press, New York, San Francisco, London, 1975. MR0450957
  2. Nečas J., Šilhavý M., Multipolar viscous fluids, Quart. of Appl. Math. XLIX (1991), 247-266. (1991) MR1106391
  3. Nečas J., Novotný A., Šilhavý M., Global solutions to the compressible isothermal multipolar fluid, J. Math. Anal. Appl. (1991). (1991) MR1135273
  4. Nečas J., Novotný A., Šilhavý M., Global solutions to the viscous compressible barotropic multipolar gas, Theoret. Comp. Fluid Dynamics 4 (1992). (1992) 
  5. Nečas J., Novotný A., Some qualitative properties of the viscous compressible heat conductive multipolar fluid, Commun. in Part. Dif. Eq. 16 (1991). (1991) MR1104099
  6. Lions J.J., Quelques méthodes de résolution des problèmes aux limites nonlinéaires, Dunod, Paris, 1969, . 
  7. Kufner A., John O., Fučík S., Functional Spaces, Academia Prague, 1977. 
  8. Málek J., Nečas J., Růžička, Measure valued solutions to nonnewtonian incompressible fluids in bounded domains, to appear. 
  9. Nečas J., Les méthodes directes en théorie des équations elliptiques, Prague, 1967. MR0227584
  10. Matušů-Nečasová Š., Global solution to the isothermal compressible bipolar fluid in a finite channel with nonzero input and output, Applications of Mathematics 36 (1991), 46-71. (1991) MR1093482
  11. Nečas J., Theory of multipolar viscous fluids, The Mathematics of Finite Elements and Applications VII (1991), 233-244. (1991) MR1132501
  12. Bellout H., Bloom R., Nečas J., Phenomenical behaviour of multipolar viscous fluid, to appear in the Quaterly Appl. Math. 
  13. Nečas J., Sur les normes équivalentes dans W p k ( Ø m e g a ) et sur la coercivité des formes formellement positives, Les presses de l'Université de Montréal, 1966. 

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