In applications in blood flow and pipeline transport, the radial length scale of the underlying flow is usually small compared to the horizontal length scale. In this talk, we will introduce a new model called the axisymmetric hydrostatic Euler equations, which describe the leading order behavior of an ideal and axisymmetric fluid moving in such narrow channel. After providing the formal derivation, we will discuss the mathematical analysis of this model under a new sign condition. This is a joint work with Robert M. Strain.
