Journal of Dynamics and Differential Equations

, Volume 18, Issue 2, pp 357–379

A Non-Newtonian Fluid with Navier Boundary Conditions

Article

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 solutions Navier boundary conditions non-newtonian third grade fluid 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Faculté des Sciences, Equipe d’analyse numériqueUniversité Jean MonnetSaint-EtienneFrance
  2. 2.Institut Camille JordanUniversité Claude Bernard Lyon 1Villeurbanne CedexFrance

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