Abstract
The Stokes flow appears in the study of phenomena across a wide range of scientific fiels (physics, biology, medicine), characterized by negligible variations in time , of the characteristic quantities . The study of the creeping incompressible flow (or Stokes flow) of a Newtonian fluid, and its Mathematical modeling lead to the partial differential equations of elliptical type involving the Stokes operator.
A complete study has been made (Hadjinicolaou 1993, Protopapas 2013) regarding 0 eigenvalue of Ε2, and the complete eigenspace and the generalized eigenspace of it has been obtained. A complete study of all non-zero eigenvalues has not been made yet, so analytical solutions for the problems at hand have not been obtained yet.
The aim of the particular PhD thesis is the study of all nonzero eigenvalues of equations E4y=lE2y and E2y=ly, and of their corresponding eigenfunspaces. This study and the results, apart from their strong mathematical interest, they are expected to be useful for treating realistic problems in the above mentioned scientific fields.
Advisory Committee
Prof. Maria Hadjinicolaou, Supervisor
Prof. Fotios Paliogiannis, Chair, S. Francis College, N.York
Prof. Vasileios Papadopoulos, Dept of Civil Engineering, Democritus University of Thrace