Applied Mathematics & Optimization

, Volume 78, Issue 2, pp 403–456 | Cite as

On the Existence, Uniqueness and Regularity of Solutions of a Viscoelastic Stokes Problem Modelling Salt Rocks

  • R. A. Cipolatti
  • I.-S. Liu
  • L. A. Palermo
  • M. A. Rincon
  • R. M. S. RosaEmail author


A Stokes-type problem for a viscoelastic model of salt rocks is considered, and existence, uniqueness and regularity are investigated in the scale of \(L^2\)-based Sobolev spaces. The system is transformed into a generalized Stokes problem, and the proper conditions on the parameters of the model that guarantee that the system is uniformly elliptic are given. Under those conditions, existence, uniqueness and low-order regularity are obtained under classical regularity conditions on the data, while higher-order regularity is proved under less stringent conditions than classical ones. Explicit estimates for the solution in terms of the data are given accordingly.


Generalized Stokes problem Elliptic regularization Viscoelastic fluids Salt modelling 

Mathematics Subject Classification

35Q30 76D06 35B40 37A60 



All the authors acknowledge the financial support of CENPES/PETROBRÁS. R.M.S. Rosa was also partly supported by CNPq, Brasília, Brazil.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • R. A. Cipolatti
    • 1
  • I.-S. Liu
    • 1
  • L. A. Palermo
    • 2
  • M. A. Rincon
    • 1
  • R. M. S. Rosa
    • 1
    Email author
  1. 1.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  2. 2.CENPES/PetrobrásRio de JaneiroBrazil

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