Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem

Petr Kaplický; Josef Málek; Jana Stará

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 4, page 681-695
  • ISSN: 0010-2628

Abstract

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We prove the existence of regular solution to a system of nonlinear equations describing the steady motions of a certain class of non-Newtonian fluids in two dimensions. The equations are completed by requirement that all functions are periodic.

How to cite

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Kaplický, Petr, Málek, Josef, and Stará, Jana. "Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem." Commentationes Mathematicae Universitatis Carolinae 38.4 (1997): 681-695. <http://eudml.org/doc/248066>.

@article{Kaplický1997,
abstract = {We prove the existence of regular solution to a system of nonlinear equations describing the steady motions of a certain class of non-Newtonian fluids in two dimensions. The equations are completed by requirement that all functions are periodic.},
author = {Kaplický, Petr, Málek, Josef, Stará, Jana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {non-Newtonian fluids; shear dependent viscosity; regularity; Hölder continuity of gradients; shear-dependent viscosity; regularity; Hölder continuous gradient; existence; incompressible non-Newtonian fluids; weak solution},
language = {eng},
number = {4},
pages = {681-695},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem},
url = {http://eudml.org/doc/248066},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Kaplický, Petr
AU - Málek, Josef
AU - Stará, Jana
TI - Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 4
SP - 681
EP - 695
AB - We prove the existence of regular solution to a system of nonlinear equations describing the steady motions of a certain class of non-Newtonian fluids in two dimensions. The equations are completed by requirement that all functions are periodic.
LA - eng
KW - non-Newtonian fluids; shear dependent viscosity; regularity; Hölder continuity of gradients; shear-dependent viscosity; regularity; Hölder continuous gradient; existence; incompressible non-Newtonian fluids; weak solution
UR - http://eudml.org/doc/248066
ER -

References

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  9. Nečas J., Sur la régularité des solutions faibles des équations elliptiques non linéaires, Comment. Math. Univ. Carolinae 9.3 (1968), 365-413. (1968) MR0241804
  10. Nečas J., Sur la régularité des solutions variationnelles des équations elliptiques nonlinéaires d’ordre 2 k en deux dimensions, Annali della Scuola Normale Superiore di Pisa XXI Fasc. III (1967), 427-457. (1967) MR0226467
  11. Stará J., Regularity results for non-linear elliptic systems in two dimensions, Annali della Scuola Normale Superiore di Pisa XXV Fasc. I (1971), 163-190. (1971) MR0299935
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