  Finite time blow up vs global regularity question for 3D Euler equation of
fluid mechanics is a major open problem. Several years ago, Luo and Hou
\cite{HouLuo14} proposed a new finite time blow up scenario based on extensive
numerical simulations. The scenario is axi-symmetric and features fast growth
of vorticity near a ring of hyperbolic points of the flow located at the
boundary of a cylinder containing the fluid. An important role is played by a
small boundary layer where intense growth is observed. Several simplified
models of the scenario have been considered, all leading to finite time blow up
\cite{CKY15,CHKLVY17,HORY,KT1,HL15,KY1}. In this paper, we propose two models
that are designed specifically to gain insight in the evolution of fluid near
the hyperbolic stagnation point of the flow located at the boundary. One model
focuses on analysis of the depletion of nonlinearity effect present in the
problem. Solutions to this model are shown to be globally regular. The second
model can be seen as an attempt to capture the velocity field near the boundary
to the next order of accuracy compared with the one-dimensional models such as
\cite{CKY15,CHKLVY17}. Solutions to this model blow up in finite time.
