On existence and regularity of solutions to a class of generalized stationary Stokes problem

Nguyen Duc Huy; Jana Stará

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 2, page 241-264
  • ISSN: 0010-2628

Abstract

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We investigate the existence of weak solutions and their smoothness properties for a generalized Stokes problem. The generalization is twofold: the Laplace operator is replaced by a general second order linear elliptic operator in divergence form and the “pressure” gradient ∇ p is replaced by a linear operator of first order.

How to cite

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Huy, Nguyen Duc, and Stará, Jana. "On existence and regularity of solutions to a class of generalized stationary Stokes problem." Commentationes Mathematicae Universitatis Carolinae 47.2 (2006): 241-264. <http://eudml.org/doc/249853>.

@article{Huy2006,
abstract = {We investigate the existence of weak solutions and their smoothness properties for a generalized Stokes problem. The generalization is twofold: the Laplace operator is replaced by a general second order linear elliptic operator in divergence form and the “pressure” gradient $\nabla p$ is replaced by a linear operator of first order.},
author = {Huy, Nguyen Duc, Stará, Jana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {generalized Stokes problem; weak solutions; regularity up to the boundary; generalized Stokes problem; weak solutions; regularity},
language = {eng},
number = {2},
pages = {241-264},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On existence and regularity of solutions to a class of generalized stationary Stokes problem},
url = {http://eudml.org/doc/249853},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Huy, Nguyen Duc
AU - Stará, Jana
TI - On existence and regularity of solutions to a class of generalized stationary Stokes problem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 2
SP - 241
EP - 264
AB - We investigate the existence of weak solutions and their smoothness properties for a generalized Stokes problem. The generalization is twofold: the Laplace operator is replaced by a general second order linear elliptic operator in divergence form and the “pressure” gradient $\nabla p$ is replaced by a linear operator of first order.
LA - eng
KW - generalized Stokes problem; weak solutions; regularity up to the boundary; generalized Stokes problem; weak solutions; regularity
UR - http://eudml.org/doc/249853
ER -

References

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  10. Stará J., Regularity results for non-linear elliptic systems in two dimensions, Ann. Scuola Norm. Sup. Pisa (3) 25 (1971), 163-190. (1971) MR0299935
  11. Hron J., Málek J., Nečas J., Rajagopal K.R., Numerical simulations and global existence of solutions of two-dimensional flows of fluids with pressure- and shear-dependent viscosities, Math. Comput. Simulation 61 3-6 (2003), 297-315. (2003) Zbl1205.76159MR1984133
  12. Málek J., Nečas J., Rajagopal K.R., Global analysis of the flows of fluids with pressure-dependent viscosities, Arch. Ration. Mech. Anal. 165 (2002), 243-269. (2002) Zbl1022.76011MR1941479
  13. Franta M., Málek J., Rajagopal K.R., On steady flows of fluids with pressure- and shear-dependent viscosities, Proc. Royal Soc. London Ser. A 461 (2005), 651-670. (2005) Zbl1145.76311MR2121929

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