, Volume 18, Issue 2, pp 357-379
Date: 12 May 2006

A Non-Newtonian Fluid with Navier Boundary Conditions

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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 H 2, 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.