On Boundary Conditions for Fluids of the Differential Type

Abstract

There have been several, recent investigations devoted to the study of the ex-istence 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 Navier-Stokes equations, we need to address the issue of whether the “no slip” boundary condition is sufficient to have a well-posed 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).