The Stokes second problem and its extension to viscoelastic fluids

Abstract

[en] This work is focused on the Stokes second problem, a classical problem in fluid mechanics. It is an oscillatory fluid flow problem of great significance both academically and practically, for its relation with industrial and natural processes. This work was inspired by the study of a viscoelastic fluid problem carried on within [4], which possesses a certain similarity with the Stokes second problem. First, we set the fundamental principles of fluid dynamics, which we need to derive the governing equations of motion of the fluid. Next, we introduce the objects used to characterise the viscous properties of fluids and to determine how these affect the motion of the fluid. In addition, a derivation of the Navier-Stokes equation is provided. Finally, we introduce and solve the Stokes second problem, justifying the existence and the uniqueness of the solution. At last, we examine the equations that model the motion of the fluid considered in [4], which can be seen as a generalisation of the Stokes second problem for a specific non-Newtonian fluid.