Fundamental solutions of linearized Navier-Stokes equations and applications

Fundamental solutions are determined for three types of linearized Navier-Stokes equations associated with three different physical situations, namely: (1) the steady flow of a viscous fluid through a porous medium, (2) the time dependent behavior of a viscous fluid for the classical flow situation as well as for flow through a porous medium, and (3) the asymptotic behavior of a slowly rotating viscous fluid. In most cases, the solutions for both types of linearizations are constructed. In addition, the resultant solutions are used to solve several viscous flow problems in which the appropriate fundamental solutions are distributed along flow boundaries and the distribution strength is determined as the solution to an integral equation which results from the application of boundary conditions.