Boundary layer models of the Hou-Luo scenario

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 [16] proposed new finite scenario based on extensive numerical simulations. The axi-symmetric features fast growth vorticity near ring hyperbolic points the flow located at boundary cylinder containing fluid. An important role played by small layer where intense observed. simplified models have been considered, all leading to [3], [2], [9], [13], [11], [15]. In this paper, we propose two that are designed specifically gain insight in evolution stagnation point boundary. One model focuses analysis depletion nonlinearity effect present Solutions shown be globally regular. second can seen as an attempt capture velocity field next order accuracy compared with one-dimensional such [2]. time.