Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind (Q2781712)

This extended paper is devoted to the mathematical theory of viscoelastic fluids of the Oldroyd kind. The authors consider successively: existence, uniqueness, regularity, well-posedness and stability results for the problems whose solutions determine the mathematical description of the flow. Chapter I contains a brief physical description of non-Newtonian fluids. Chapter II is devoted to the study of the so-called evolution problem for viscoelastic fluids of Oldroyd kind. More precisely, the existence, uniqueness, regularity, and stability of the solution to the time-dependent problem are analyzed. The stationary problem, i.e. the time-independent solutions of the evolution problem from chapter II, is considered in chapter III. The existence, uniqueness and regularity of the solutions are proved for small data. The last chapter considers several particular flows: the axisymmetric and plane Poiseuille flows, and the plane Couette flow for viscoelastic fluid of Oldroyd kind.NEWLINENEWLINEFor the entire collection see [Zbl 0978.00020].