Journal of Mathematical Fluid Mechanics

, Volume 13, Issue 3, pp 387–404 | Cite as

Boundary Regularity of Shear Thickening Flows

  • Hugo Beirão da Veiga
  • Petr Kaplický
  • Michael Růžička


This article is concerned with the global regularity of weak solutions to systems describing the flow of shear thickening fluids under the homogeneous Dirichlet boundary condition. The extra stress tensor is given by a power law ansatz with shear exponent p≥ 2. We show that, if the data of the problem are smooth enough, the solution u of the steady generalized Stokes problem belongs to \({W^{1,(np+2-p)/(n-2)}(\Omega)}\) . We use the method of tangential translations and reconstruct the regularity in the normal direction from the system, together with anisotropic embedding theorem. Corresponding results for the steady and unsteady generalized Navier–Stokes problem are also formulated.

Mathematics Subject Classification (2000)

35Q35 35J65 76D03 


Generalized Newtonian fluids shear dependent viscosity regularity up to the boundary 


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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  • Hugo Beirão da Veiga
    • 1
  • Petr Kaplický
    • 2
  • Michael Růžička
    • 3
  1. 1.Department of Applied Mathematics “U. Dini”Pisa UniversityPisaItaly
  2. 2.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic
  3. 3.Mathematisches InstitutUniversität FreiburgFreiburgGermany

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