Revisiting Stokes first and second problems for fluids with pressure-dependent viscosities

Abstract

We revisit the numerical study carried out by Srinivasan and Rajagopal [1] and we show that the long time solutions to the first and second Stokes problem for fluids with pressure dependent viscosities can be given by exact formulae. Moreover we show that the transient solutions – thus for example the solutions studied by numerical means by Srinivasan and Rajagopal [1] – must rapidly converge to these long time solutions.

Keywords

• Pressure-dependent viscosity
• Stokes first problem
• Stokes second problem
• Exact solution