Geotechnical engineers design and analyze the interface between the natural and built environments, often based on uncertain and inherently variable data due to the nature of the building material, soil. Engineers must estimate the subsurface conditions at a site using historical, in-situ, and laboratory testing data. However, only discrete representative...
In this dissertation, we use Fourier-analytic and spectral theory methods to analyze the behavior of solutions of the incompressible Navier-Stokes equations in 2D and 3D (with an eye towards better understanding turbulence). In particular, we investigate the possible existence of so-called ghost solutions to the Navier-Stokes Equations. Such solutions, if...