Doctoral Dissertation Defense: Randy Price

In the first part of the presentation, we consider data assimilation for Navier-Stokes equations, the governing equation of motion for incompressible, Newtonian fluids. We consider the so- called nudging data assimilation algorithm applied to the 3D Navier-Stokes equations and we derive conditions, based entirely on the observations, that guarantee the global well- posedness, the regularity, and the tracking property of the nudging solution, in case the observations from the model are exact. We then do a computational study that compares the nudging and ensemble Kalman filter. Time permitting, we will also discuss the case where the observations as well as the model are subject to stochastic errors.  

In the second part of the talk we study the 2D Navier-Stokes equations with random viscosity. This is done with stochastic finite element discretizations and generalized polynomial chaos. Finally we study the linear stability of solutions to the 2D stochastic Navier-Stokes equations with random viscosity.