On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity

Hiroshi Kawabi

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 1, page 161-178
  • ISSN: 0010-2628

Abstract

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In this paper, we prove that the regularity property, in the sense of Gehring-Giaquinta-Modica, holds for weak solutions to non-stationary Stokes type equations. For the construction of solutions, Rothe's scheme is adopted by way of introducing variational functionals and of making use of their minimizers. Local estimates are carried out for time-discrete approximate solutions to achieve the higher integrability. These estimates for gradients do not depend on approximation.

How to cite

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Kawabi, Hiroshi. "On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity." Commentationes Mathematicae Universitatis Carolinae 46.1 (2005): 161-178. <http://eudml.org/doc/249536>.

@article{Kawabi2005,
abstract = {In this paper, we prove that the regularity property, in the sense of Gehring-Giaquinta-Modica, holds for weak solutions to non-stationary Stokes type equations. For the construction of solutions, Rothe's scheme is adopted by way of introducing variational functionals and of making use of their minimizers. Local estimates are carried out for time-discrete approximate solutions to achieve the higher integrability. These estimates for gradients do not depend on approximation.},
author = {Kawabi, Hiroshi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {non-stationary Stokes type equations; higher integrability of gradients; Caccioppoli type estimate; Gehring theory; Rothe's scheme; Caccioppoli type estimate; Gehring theory; Rothe's scheme},
language = {eng},
number = {1},
pages = {161-178},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity},
url = {http://eudml.org/doc/249536},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Kawabi, Hiroshi
TI - On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 1
SP - 161
EP - 178
AB - In this paper, we prove that the regularity property, in the sense of Gehring-Giaquinta-Modica, holds for weak solutions to non-stationary Stokes type equations. For the construction of solutions, Rothe's scheme is adopted by way of introducing variational functionals and of making use of their minimizers. Local estimates are carried out for time-discrete approximate solutions to achieve the higher integrability. These estimates for gradients do not depend on approximation.
LA - eng
KW - non-stationary Stokes type equations; higher integrability of gradients; Caccioppoli type estimate; Gehring theory; Rothe's scheme; Caccioppoli type estimate; Gehring theory; Rothe's scheme
UR - http://eudml.org/doc/249536
ER -

References

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  10. Kawabi H., On a construction of weak solutions to non-stationary Navier-Stokes type equations via Rothe's scheme and their regularity, preprint, 2004. 
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  15. Naumann J., Wolff M., Interior integral estimates on weak solutions of nonlinear parabolic systems, Institut für Mathematik der Humboldt-Universität zu Berlin, 1994, preprint 94-12. 
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