Abstract
We investigate the accuracy of two mean-field theories of the trapped two-dimensional Bose gas at predicting transition region properties by comparison to nonperturbative classical field calculations. To make these comparisons we examine the density profiles and the predictions for the Berezinskii-Kosterlitz-Thouless superfluid transition temperature over a parameter range in which the degree of thermal activation in the tightly trapped direction varies considerably. These results present an important test of these mean-field theories and provide a characterization of their typical accuracy.