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Hölder continuity of velocity gradients for shear-thinning fluids under perfect slip boundary conditions

  • Václav MáchaEmail author
  • Jakub Tichý
Article

Abstract

This paper is concerned with non-stationary flows of shear-thinning fluids in a bounded two-dimensional \(\mathcal {C}^{2,1}\) domain. Assuming perfect slip boundary conditions, we provide a proof of the existence of a solution with the Hölder continuous velocity gradients and pressure under condition that a stress tensor satisfies power-law with growth \(p\in [5/3;2]\).

Keywords

Generalized Newtonian fluid Regularity up to the boundary Perfect slip boundary conditions 

Mathematics Subject Classification

35B65 35K51 35Q35 76D03 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Industry-University Research CenterYonsei UniversitySeoulRepublic of Korea
  2. 2.Faculty of Information TechnologyCzech Technical University in PraguePrague 6Czech Republic

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