On Boundary Conditions for Fluids of the Different

Authors: K R Rajagopal

Publish Date: 1995

Volume: , Issue: , Pages: 273-278

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Abstract

There have been several recent investigations devoted to the study of the existence and uniqueness of solutions to the equations governing the flows of fluids of the differential type As these equations are usually higher order partial differential equations than the NavierStokes equations we need to address the issue of whether the “no slip” boundary condition is sufficient to have a wellposed problem While this issue has been raised earlier see Rajagopal 1984 Rajagopal and Kaloni 1989 Rajagopal 1992 and Rajagopal and Gupta 1984 given the critical role it plays in shaping the theory it has not been accorded the importance it deserves This question cannot be answered in any generality for fluids of the differential type of complexity n for arbitrary n However if attention is confined to fluids of grade 2 or grade 3 we can indeed provide some definitive answers while some partial answers are possible for fluids of grade n Rajagopal 1984

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