Journal of Dynamics and Differential Equations

, Volume 18, Issue 2, pp 357–379

A Non-Newtonian Fluid with Navier Boundary Conditions

Authors

  • Adriana Valentina Busuioc
    • Faculté des Sciences, Equipe d’analyse numériqueUniversité Jean Monnet
    • Institut Camille JordanUniversité Claude Bernard Lyon 1
Article

DOI: 10.1007/s10884-006-9008-3

Cite this article as:
Busuioc, A.V. & Iftimie, D. J Dyn Diff Equat (2006) 18: 357. doi:10.1007/s10884-006-9008-3

Abstract

We consider in this paper the equations of motion of third grade fluids on a bounded domain of \(\mathbb{R}^2\) or \(\mathbb{R}^3\) with Navier boundary conditions. Under the assumption that the initial data belong to the Sobolev space H2, we prove the existence of a global weak solution. In dimension two, the uniqueness of such solutions is proven. Additional regularity of bidimensional initial data is shown to imply the same additional regularity for the solution. No smallness condition on the data is assumed.

Keywords

Global weak solutionsNavier boundary conditionsnon-newtonianthird grade fluid

Copyright information

© Springer Science+Business Media, Inc. 2006