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On the global existence for a regularized model of viscoelastic non-Newtonian fluid

Volume 139 / 2015

Ondřej Kreml, Milan Pokorný, Pavel Šalom Colloquium Mathematicum 139 (2015), 149-163 MSC: Primary 35Q35; Secondary 76D03. DOI: 10.4064/cm139-2-1

Abstract

We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like $\mu (\mathbf {D}) \sim | \mathbf {D} |^{p-2}$ ($p>{6/5}$), regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we prove global existence of a weak solution to the corresponding system of partial differential equations.

Authors

  • Ondřej KremlInstitute of Mathematics
    Academy of Sciences of the Czech Republic
    Žitná 25
    115 65 Praha 1, Czech Republic
    e-mail
  • Milan PokornýMathematical Institute
    Faculty of Mathematics and Physics
    Charles University in Prague
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail
  • Pavel ŠalomDepartment of Mathematics Education
    Faculty of Mathematics and Physics
    Charles University in Prague
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail

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