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Existence and Uniqueness of the Flow of Second‐Grade Fluids with Slip Boundary Conditions

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Abstract

. This paper treats the solvability of the equations of motion for an incompressible fluid of grade two subject to nonlinear partial slip boundary conditions in a bounded simply‐connected domain. The existence of a unique classical solution, global in time, is proved under suitable regularity and growth restrictions on the initial data, the slip law and the body and surface forces. The method is based on a fixed-point formulation of the problem.

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Authors and Affiliations

  1. Department of Quantitative Management, University of South Africa, PO Box 392, Pretoria 0003, South Africa, e‐mail: lrouxc@alpha.unisa.ac.za, , , , , , ZA

    Christiaan le Roux

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  1. Christiaan le Roux
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(Accepted October 5, 1998)

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le Roux, C. Existence and Uniqueness of the Flow of Second‐Grade Fluids with Slip Boundary Conditions. Arch Rational Mech Anal 148, 309–356 (1999). https://doi.org/10.1007/s002050050164

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  • DOI: https://doi.org/10.1007/s002050050164

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