UC Riverside

One open question in the study of the steady incompressible three-dimensional Navier-Stokes equations is if the only solution with finite Dirichlet integral and vanishing condition at infinity is the trivial solution. Several partial results have been proven by requiring certain integral or decay conditions on the solution. We will explore a certain class of solutions, called axially-symmetric D-solutions, and discuss some results about these solutions. In this thesis, we will prove that certain axially-symmetric periodic D-solutions are identicially zero.