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

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)161-178
Number of pages18
JournalCommentationes Mathematicae Universitatis Carolinae
Volume46
Issue number1
Publication statusPublished - 2005 Jan 1
Externally publishedYes

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Stokes
Weak Solution
Regularity
Regularity Properties
Minimizer
Estimate
Integrability
Discrete-time
Approximate Solution
Gradient
Approximation

Keywords

  • Caccioppoli type estimate
  • Gehring theory
  • Higher integrability of gradients
  • Non-stationary Stokes type equations
  • Rothe's scheme

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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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.",
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