On Some Weighted Stokes Problems: Applications on Smagorinsky Models

  • Jacques RappazEmail author
  • Jonathan Rochat
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 47)


In this paper we study existence and uniqueness of weak solutions for some non-linear weighted Stokes problems using convex analysis. The characterization of these equations is the viscosity, which depends on the strain rate of the velocity field and in some cases is related with a weight being the distance to the boundary of the domain. Such non-linear relations can be seen as a first approach of mixing-length eddy viscosity from turbulent modeling. A well known model is von Karman’s on which the viscosity depends on the square of the distance to the boundary of the domain. Numerical experiments conclude the work and show properties from the theory.


Stokes equations Weighted Sobolev spaces Finite element method 

Mathematical Subject Classification

46E35 76F55 65N05 



The authors would like to thank Rio-Tinto Alcan Company for their financial support and Agnieska Kalamaskya for her input on Korn’s Inequalities.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland

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