Mathematical Issues Concerning the Navier-Stokes Equations and Some of Its Generalizations

Abstrakt

This article primarily deals with internal, isothermal, unsteady flows of a class of incompressible fluids with both constant, and shear or pressure dependent viscosity that includes the Navier-Stokes fluid as a special subclass. The first part provides a description of fluids within the framework of a continuum.

Second part is focused on the mathematical analysis of three-dimensional unsteady flows of fluids with shear dependent viscosity that includes the Navier-Stokes model and Ladyshenskaya's model as special cases.